AP14870431 «Haagerup Noncommutative Orlicz Spaces and Applications»
Project Objective
The project aims to define Haagerup noncommutative Orlicz spaces as analogues of classical spaces used in functional analysis. It studies key theoretical results such as reduction and duality theorems. The research extends martingale inequalities from the classical (tracial) setting to the noncommutative case. In addition, it introduces noncommutative Orlicz–Hardy spaces and investigates factorization properties, invariant subspaces, and the characterization of outer operators.
Task 1. Define noncommutative Orlicz spaces associated with a given algebra and state, show that they generalize known spaces, and prove their consistency with classical cases.
Task 2. Extend the reduction theorem to Orlicz spaces, establish duality results, and prove that these spaces do not depend on the choice of state up to isometric equivalence.
Task 3. Extend martingale inequalities from the classical setting to the noncommutative setting, generalizing known results for noncommutative martingales.
Task 4. Study special subsets of these spaces with integrability properties and prove a decomposition (splitting) result for subsequences.
Task 5. Define noncommutative Orlicz–Hardy spaces and establish factorization theorems, results on invariant subspaces, and provide a characterization of outer operators.
Task 1. Define noncommutative Orlicz spaces associated with a given algebra and state, show that they generalize known spaces, and prove their consistency with classical cases.
Task 2. Extend the reduction theorem to Orlicz spaces, establish duality results, and prove that these spaces do not depend on the choice of state up to isometric equivalence.
Task 3. Extend martingale inequalities from the classical setting to the noncommutative setting, generalizing known results for noncommutative martingales.
Task 4. Study special subsets of these spaces with integrability properties and prove a decomposition (splitting) result for subsequences.
Task 5. Define noncommutative Orlicz–Hardy spaces and establish factorization theorems, results on invariant subspaces, and provide a characterization of outer operators.
Project Relevance:
The expected scientific results of the project are primarily of a fundamental nature. Overall, the project is aimed at advancing mathematical methods within the qualitative theory of noncommutative analysis. Its implementation will contribute to the comprehensive development of classical theory and will define new directions for further research.
During the implementation of the project, the scientific qualifications of the research team in the field of noncommutative analysis, in line with international standards, will be enhanced. The project will increase the interest of domestic mathematicians working in higher education and science in this research area, improve the competitiveness of research teams, and thereby positively influence the further development of mathematical research and higher education in the country. At the same time, the expected social and economic impact of the project lies in strengthening the intellectual potential of the country. This impact will also be reflected in the future through the study of theoretical problems of noncommutative analysis and potential practical applications arising from them, based on the results, methods, and ideas of the project.
We are confident that the project will open new opportunities for strengthening international scientific collaboration. As evidenced by the review of prior work, research in this field is активно conducted in countries such as the USA, France, Japan, and China. The research team has experience in collaboration with scientists from the University of Franche-Comté (France), Wuhan Institute of Physics and Mathematics of the Chinese Academy of Sciences, Xinjiang University (China), the University of New South Wales (Australia), and others. Thus, the implementation of the project fully aligns with the objectives of the State Program for the Development of Education and Science of the Republic of Kazakhstan for 2020–2025: enhancing the global competitiveness of Kazakhstan’s education and science and increasing the contribution of science to the country’s socio-economic development.
The expected scientific results of the project are primarily of a fundamental nature. Overall, the project is aimed at advancing mathematical methods within the qualitative theory of noncommutative analysis. Its implementation will contribute to the comprehensive development of classical theory and will define new directions for further research.
During the implementation of the project, the scientific qualifications of the research team in the field of noncommutative analysis, in line with international standards, will be enhanced. The project will increase the interest of domestic mathematicians working in higher education and science in this research area, improve the competitiveness of research teams, and thereby positively influence the further development of mathematical research and higher education in the country. At the same time, the expected social and economic impact of the project lies in strengthening the intellectual potential of the country. This impact will also be reflected in the future through the study of theoretical problems of noncommutative analysis and potential practical applications arising from them, based on the results, methods, and ideas of the project.
We are confident that the project will open new opportunities for strengthening international scientific collaboration. As evidenced by the review of prior work, research in this field is активно conducted in countries such as the USA, France, Japan, and China. The research team has experience in collaboration with scientists from the University of Franche-Comté (France), Wuhan Institute of Physics and Mathematics of the Chinese Academy of Sciences, Xinjiang University (China), the University of New South Wales (Australia), and others. Thus, the implementation of the project fully aligns with the objectives of the State Program for the Development of Education and Science of the Republic of Kazakhstan for 2020–2025: enhancing the global competitiveness of Kazakhstan’s education and science and increasing the contribution of science to the country’s socio-economic development.
Expected Results
As a result of the project, we will define Haagerup noncommutative Orlicz spaces associated with a von Neumann algebra and a given state, which serve as analogues of classical spaces. We will prove that these Orlicz spaces coincide with the standard tracial case. Furthermore, we will establish the Haagerup reduction theorem and the duality theorem, and demonstrate that these spaces do not depend on the choice of state up to isometric isomorphism. We will extend certain martingale inequalities from the tracial setting to Haagerup noncommutative Orlicz spaces. It is expected that we will characterize special equiintegrable subsets of these spaces and prove a subsequence splitting lemma. In addition, we will define noncommutative Orlicz–Hardy spaces and establish Riesz-type and Szegő-type factorization theorems. We will also derive Beurling–Blecher–Labuschagne-type results for invariant subspaces and provide a characterization of outer operators in these spaces.
All the expected results of this project are novel. They are anticipated to make a significant contribution to the development of noncommutative Orlicz spaces, noncommutative Hardy spaces, and martingale theory.
As a result of the project, we will define Haagerup noncommutative Orlicz spaces associated with a von Neumann algebra and a given state, which serve as analogues of classical spaces. We will prove that these Orlicz spaces coincide with the standard tracial case. Furthermore, we will establish the Haagerup reduction theorem and the duality theorem, and demonstrate that these spaces do not depend on the choice of state up to isometric isomorphism. We will extend certain martingale inequalities from the tracial setting to Haagerup noncommutative Orlicz spaces. It is expected that we will characterize special equiintegrable subsets of these spaces and prove a subsequence splitting lemma. In addition, we will define noncommutative Orlicz–Hardy spaces and establish Riesz-type and Szegő-type factorization theorems. We will also derive Beurling–Blecher–Labuschagne-type results for invariant subspaces and provide a characterization of outer operators in these spaces.
All the expected results of this project are novel. They are anticipated to make a significant contribution to the development of noncommutative Orlicz spaces, noncommutative Hardy spaces, and martingale theory.
Project Achievements
The research project is planned for 2022–2024. According to the approved project timeline, three scientific articles have currently been published in journals indexed in the Web of Science database (Q2–Q3 quartiles), and the research team has participated in three international scientific conferences with presentations.
1. Turdebek N. Bekjan, Manat Mustafa, Dominated convergence theorems in Haagerup noncommutative Lp-spaces. Advances in Operator Theory, 8, Article number: 34, 2023 (Q2). https://doi.org/10.1007/s43036-023-00261-1
2. Turdebek N. Bekjan, Noncommutative symmetric space associated with the weight. SCIENTIA SINICA Mathematica, 2023 (Q4, accepted for publication). https://doi.org/10.1360/SSM-2022-0226
3. M. Alday, S. Kudaibergenov, On submajorization of the Rotfeld’s inequality. FILOMAT, 37(21), 2023 (accepted for publication).
Conference presentations:
4. Bekjan T.N., Szegő type factorization of Haagerup noncommutative Hardy spaces. April International Mathematical Conference dedicated to the Day of Scientific Workers of the Republic of Kazakhstan, p. 129, Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan, April 5–7, 2023.
5. Raikhan M., Zhalgas A., On some inequalities for positive matrix of τ-measurable operators. April International Mathematical Conference dedicated to the Day of Scientific Workers of the Republic of Kazakhstan, p. 129, Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan, April 5–7, 2023.
6. Alday M., Sotsial Z., Yelemes T., On submajorisation of the Rotfeld’s inequality. April International Mathematical Conference dedicated to the Day of Scientific Workers of the Republic of Kazakhstan, p. 31, Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan, April 5–7, 2023.
1. Turdebek N. Bekjan, Manat Mustafa, Dominated convergence theorems in Haagerup noncommutative Lp-spaces. Advances in Operator Theory, 8, Article number: 34, 2023 (Q2). https://doi.org/10.1007/s43036-023-00261-1
2. Turdebek N. Bekjan, Noncommutative symmetric space associated with the weight. SCIENTIA SINICA Mathematica, 2023 (Q4, accepted for publication). https://doi.org/10.1360/SSM-2022-0226
3. M. Alday, S. Kudaibergenov, On submajorization of the Rotfeld’s inequality. FILOMAT, 37(21), 2023 (accepted for publication).
Conference presentations:
4. Bekjan T.N., Szegő type factorization of Haagerup noncommutative Hardy spaces. April International Mathematical Conference dedicated to the Day of Scientific Workers of the Republic of Kazakhstan, p. 129, Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan, April 5–7, 2023.
5. Raikhan M., Zhalgas A., On some inequalities for positive matrix of τ-measurable operators. April International Mathematical Conference dedicated to the Day of Scientific Workers of the Republic of Kazakhstan, p. 129, Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan, April 5–7, 2023.
6. Alday M., Sotsial Z., Yelemes T., On submajorisation of the Rotfeld’s inequality. April International Mathematical Conference dedicated to the Day of Scientific Workers of the Republic of Kazakhstan, p. 31, Institute of Mathematics and Mathematical Modeling, Almaty, Kazakhstan, April 5–7, 2023.
Research Team Members
Nurlybekuly Turdebek (publishes as Turdebek N. Bekjan) – Project Scientific Supervisor, Chief Researcher, PhD in Mathematics.
h-index: 9 (Scopus: https://www.scopus.com/authid/detail.uri?authorId=6506605539 ), total citations: 219.
Research interests: functional analysis, noncommutative theory of symmetric spaces, noncommutative Hardy spaces, noncommutative martingale theory. He has published more than 70 scientific papers, including over 19 in the project area. He previously led one grant-funded research project (2015–2017), which was successfully completed with results published in peer-reviewed journals. He is actively involved in training scientific personnel and has supervised 10 PhD graduates. Over the past 3 years, he has published 2 papers in Q1 journals indexed in Web of Science.
Key publications related to the project area:
1. N. Bekjan and Myrzagali N. Ospanov, On Young-type inequalities of measurable operators, Linear and Multilinear Algebra (2021). https://doi.org/10.1080/03081087.2021.1920877
2. T. N. Bekjan and Myrzagali N. Ospanov, On products of noncommutative symmetric quasi Banach spaces and applications, Positivity, 25(1)(2021), 121-148. https://doi.org/10.1007/s11117-020-00753-x
3. T. N. Bekjan and K. N. Ospanov, Complex interpolation of noncommutative Hardy spaces associated semifinite von Neumann algebra, Acta Math. Sci. 40B(1) (2020), 245-260. https://doi.org/10.1007/s10473-020-0117-9
4. T. N. Bekjan and M. Zhaxylykova, Some properties of semifinite tracial subalgebras, Linear and Multilinear Algebra 67:6 (2019), 1190-1197.https://doi.org/10.1080/03081087.2018.1450349
5. T. N. Bekjan and B. K. Sageman, A property of conditional expectation, Positivity, 22(5)(2018), 1359-1369. https://doi.org/10.1007/s11117-018-0581-6
6. T. N. Bekjan, Duality for symmetric Hardy spaces of noncommutative martingales, Math. Z., 289 (2018), 787-802. https://doi.org/10.1007/s00209-017-1974-0
7. T. N. Bekjan, Duality for symmetric Hardy spaces of noncommutative martingales, Math. Z., 289 (2018), 787-802. https://doi.org/10.1007/s00209-017-1974-0
8. T. N. Bekjan, Interpolation of noncommutative symmetric martingale spaces, J. Operator Theory 77 (2017), 245-259. https://doi: 10.7900/jot.2015nov01.2142
9. T. N. Bekjan, Szego type factorization of Haagerup noncommutative Hardy spaces, Acta Mathematica Scientia 37(5) (2017), 1221-1229. https://doi.org/10.1016/S0252-9602(17)30069-3 10. T. N. Bekjan, Z. Chen and A. Osekowski, Noncommutative maximal inequalities with associated with convex functions, Trans. Amer. Math. Soc. 369(1) (2017), 409-427. http://dx.doi.org/10.1090/tran/6663
11. T. N. Bekjan, A submajorization of Carlen and Lieb convexity, Linear Algebra and pplications 494 (2016), 23-31. https://doi.org/10.1016/j.laa.2015.12.026
12. T. N. Bekjan, Noncommutative Hardy space associated with semi-finite subdiagonal algebras, J. Math. Anal. Appl. 429 (2015), 1347-1369. https://doi.org/10.1016/j.jmaa.2015.04.032
13. T. N. Bekjan, Noncommutative symmetric Hardy spaces, Inter. Equat. Oper. Th. 81 (2015), 191-212. https://doi.org/10.1007/s00020-014-2201-6
14. A. Adurexit and T. N. Bekjan, Noncommutative Orlicz-Hardy spaces, Acta Math. Sinica 34B (2014), 1584-1592. https://doi.org/10.1016/S0252-9602(14)60105-3
15. A. Adurexit and T. N. Bekjan, Noncommutative Orlicz-Hardy spaces associated with growth functions, J. Math. Anal. Appl 420 (2014), 824-834. https://doi.org/10.1016/j.jmaa.2014.06.018
16. T. N. Bekjan and Z. Chen, Interpolation and-moment inequalities of noncommutative martingales, Probab. Theory Relat. Fields 152 (2012), 179-206. https://doi.org/10.1007/s00440-010-0319-2
17. T. N. Bekjan, Z. Chen, P. Liu, Y. Jiao, Noncommutative weak Orlicz spaces and martingale inequalities, Studia Math. 204(3) (2011), 195-212. https://doi.org/10.4064/sm204-3-1
18. T. N. Bekjan, Z. Chen, M. Perrin, and Z. Yin, Atomic decomposition and interpolation for Hardy spaces of noncommutative martingales, J. Funct. Anal. 258 (2010), 2483-2505. https://doi.org/10.1016/j.jfa.2009.12.006
19. T. N. Bekjan, -inequalities of noncommutative martingales, Rocky Mountain J. Math. 36 (2) (2006), 401-412. http://www.jstor.org/stable/44239119
Madi Raikhan, Chief Researcher, holds a degree in Mathematics, Candidate of Physical and Mathematical Sciences.
h-index: 2 (Scopus: https://www.scopus.com/authid/detail.uri?authorId=55945027400 ).
Research interests: operator theory, operator algebras, functional analysis. He has published 20 scientific papers, including 10 in the project area. He has served as a scientific supervisor of grant-funded research projects during 2018–2023.
Key publications related to the project area:
1. T. N. Bekjan, Madi Raikhan, On noncommutative weak Orlicz-Hardy spaces, Ann. Funct. Anal. 13, 7(2022). https://doi.org/10.1007/s43034-021-00150-9
2. T. N. Bekjan, Zeqian Chen, Madi Raikhan and Mu Sun, Interpolation and the John-nirenberg inequality on symmetric spaces of noncommutative martingales, Studia Mathematica, 262(3) (2022), 241-273. https://doi.org/10.4064/sm200508-11-12
3. R. Ahat, M. Raikhan, Submajorization inequalities for matrices of ¦У-measurable operators, Linear and Multilinear Algebrathis (2020), https://doi.org/10.1080/03081087.2020.1828248
4. T. N. Bekjan, Madi Raikhan, A Beurling-Blecher-Labuschagne type theorem for Haagerup noncommutative spaces, Banach J. Math. Anal. 15, 39 (2021).https://doi.org/10.1007/s43037-021-00121-1
5. T. N. Bekjan, Madi Raikhan, Interpolation of Haagerup noncommutative Hardy spaces, Banach J. Math. Anal. 13 (2019), no. 4, 798-814. https://doi.org/10.1215/17358787-2018-0026
6. K.S. Tulenov and M. Raikhan, Outer operators for the noncommutative symmetric Hardy spaces with finite subdiagonal algebras, Acta Mathematica Scientia 37(3) (2017), 799-805. https://doi.org/10.1016/S0252-9602(17)30038-3
7. S. Junis and M. Raikhan, A-invariant subspaces of noncommutative Orlicz spaces, J. Xinjiang Univ. Nat. Sci. 33(3) (2016), 301-306.
8. T. N. Bekjan and Madi Raikhan, An Hadamard-type inequality, Linear Algebra and Applications 443 (2014), 228-234. https://doi.org/10.1016/j.laa.2013.11.019
9. N. Biyarov and M. Raikhan, Nonselfadjoint correct restrictions and extensions with the real spectrum, AIP Conference Proceedings 1611, 138 (2014). https://doi.org/10.1063/1.4893818
Dauitbek Dostilek, Leading Researcher, PhD, with over 10 years of experience in the project field.
He has published more than 20 original scientific papers, including 8 related to the project area. He has experience both as a project leader and as a research team member. He led a grant-funded project for young scientists during 2021–2023.
1. D. Dauitbek and K. Tulenov. Conditional expectation on non-commutative, $H_p^{(r,s)}(\A;\ell_\8)$ and $H_p(\A;\ell_1)$ spaces: semifinite case, Ann. Funct. Anal. 11(3) (2020), 617-625. https://doi.org/10.1007/s43034-019-00042-z
2. D. Dauitbek, J. Huang and F. Sukochev, Extreme points of the set of elements majorised by an integrablefunction: Resolution of a problem by Luxemburg, Advances in Mathematics 365 (2020) , No. 107050, 1-27. http://dx.doi.org/10.1016/j.aim.2020.107050
3. D. Dauitbek, Submajorization inequalities for measurable operators, AIP Conference Proceedings 1676, No. 020039 (2015), 1-5. https://doi.org/10.1063/1.4930465
4. T. N. Bekjan, D. Dauitbek, Submajorization inequalities of $\tau$-measurable operators for concave and convex functions, Positivity 19 (2) (2015), 341-345. https://doi.org/10.1007/s11117-014-0300-x
5. T. N. Bekjan, K. Tulenov and D. Dauitbek, The noncommutative $H^{(r,s)}_{p}(\A;\ell_{\infty})$ and $H_{p}(\A;\ell_{1})$ spaces, Positivity 19(4) (2015), 877-891. https://doi.org/10.1007/s11117-015-0332-x
6. D. Dauitbek, N. E. Tokmagambetov and K. S. Tulenov, Commutator inequalities associated with polar decompositions of $\tau$-measurable operators, Russian Math. (Iz. VUZ) 58 (7) (2014), 48-52. https://doi.org/10.3103/S1066369X14070056
7. T. N. Bekjan and Dostilek Dauitbek, Submajorization inequalities of measurable operators, AIP Conference Proceedings 1611, 145 (2014); https://doi.org/10.1063/1.4893820
8. Dauitbek, A. M. Tleulessova , Non-commutative Clarkson inequalities for symmetric space norm of $\tau$-measurable operators, Int. Journal of Math. Analysis 7(18) (2013), 883-890. http://dx.doi.org/10.12988/ijma.2013.13085
Maktagul Alday, Senior Researcher, Candidate of Physical and Mathematical Sciences.
She has published more than 20 original scientific papers and has experience working as a researcher in scientific projects.
1. M. Alday, A.I. Ibatov, Z.S. Aldiyarova, Methods for solving basic equations of Mathematical physics, L. N. Gumilyov ENU, 2020. P. 212
2. M. Alday, K.R. Myrzataeva, Introduction to ordinary differential equations, L. N. Gumilyov ENU, 2018. P. 212
3. M. Alday, K.R. Myrzataeva, A. Eskermesuly, Oscillatory properties of a Class of Fourth-Order Differential Equation, ENU Habarshy 6 (121) (2017), 5-13.
4. M. Alday, Bayarystanov A.O., Ramazanova K.S. Focuslessness conditions for one class of second-order semilinear differential equations on a given interval, ENU Habarshy 6(109) (2015), 5-11.
Azhar Uatayeva (Oshanova), Junior Researcher, early-career scientist, PhD doctoral student.
She has published two scientific papers in the project area and possesses sufficient expertise in the project topic. She participated in the implementation of three grant-funded research projects during 2017–2021.
Key publications related to the project area:
1. S. Junis and A. Oshanova, On submajorization inequalities for matrices of measurable operators, DOI: 10.1007/s43036-020-00101-6, to appear in Advances in Operator Theory.
2. T. N. Bekjan and A. Oshanova, Semifinite tracial subalgebras, Annals of Functional Analysis, 8(4) (2017), 473–478. http://doi.org/10.1215/20088752-2017-0011
Aidana Zhalgas, Junior Researcher, early-career scientist. Author of more than two original scientific publications and has experience as a research project participant.
Tolkynai Elemes, Junior Researcher, early-career scientist. Author of more than two original scientific publications and has experience in research project implementation.
Zhuldyz Sotsial, Junior Researcher, early-career scientist. Author of more than two original scientific publications and has experience as a research project participant.
h-index: 9 (Scopus: https://www.scopus.com/authid/detail.uri?authorId=6506605539 ), total citations: 219.
Research interests: functional analysis, noncommutative theory of symmetric spaces, noncommutative Hardy spaces, noncommutative martingale theory. He has published more than 70 scientific papers, including over 19 in the project area. He previously led one grant-funded research project (2015–2017), which was successfully completed with results published in peer-reviewed journals. He is actively involved in training scientific personnel and has supervised 10 PhD graduates. Over the past 3 years, he has published 2 papers in Q1 journals indexed in Web of Science.
Key publications related to the project area:
1. N. Bekjan and Myrzagali N. Ospanov, On Young-type inequalities of measurable operators, Linear and Multilinear Algebra (2021). https://doi.org/10.1080/03081087.2021.1920877
2. T. N. Bekjan and Myrzagali N. Ospanov, On products of noncommutative symmetric quasi Banach spaces and applications, Positivity, 25(1)(2021), 121-148. https://doi.org/10.1007/s11117-020-00753-x
3. T. N. Bekjan and K. N. Ospanov, Complex interpolation of noncommutative Hardy spaces associated semifinite von Neumann algebra, Acta Math. Sci. 40B(1) (2020), 245-260. https://doi.org/10.1007/s10473-020-0117-9
4. T. N. Bekjan and M. Zhaxylykova, Some properties of semifinite tracial subalgebras, Linear and Multilinear Algebra 67:6 (2019), 1190-1197.https://doi.org/10.1080/03081087.2018.1450349
5. T. N. Bekjan and B. K. Sageman, A property of conditional expectation, Positivity, 22(5)(2018), 1359-1369. https://doi.org/10.1007/s11117-018-0581-6
6. T. N. Bekjan, Duality for symmetric Hardy spaces of noncommutative martingales, Math. Z., 289 (2018), 787-802. https://doi.org/10.1007/s00209-017-1974-0
7. T. N. Bekjan, Duality for symmetric Hardy spaces of noncommutative martingales, Math. Z., 289 (2018), 787-802. https://doi.org/10.1007/s00209-017-1974-0
8. T. N. Bekjan, Interpolation of noncommutative symmetric martingale spaces, J. Operator Theory 77 (2017), 245-259. https://doi: 10.7900/jot.2015nov01.2142
9. T. N. Bekjan, Szego type factorization of Haagerup noncommutative Hardy spaces, Acta Mathematica Scientia 37(5) (2017), 1221-1229. https://doi.org/10.1016/S0252-9602(17)30069-3 10. T. N. Bekjan, Z. Chen and A. Osekowski, Noncommutative maximal inequalities with associated with convex functions, Trans. Amer. Math. Soc. 369(1) (2017), 409-427. http://dx.doi.org/10.1090/tran/6663
11. T. N. Bekjan, A submajorization of Carlen and Lieb convexity, Linear Algebra and pplications 494 (2016), 23-31. https://doi.org/10.1016/j.laa.2015.12.026
12. T. N. Bekjan, Noncommutative Hardy space associated with semi-finite subdiagonal algebras, J. Math. Anal. Appl. 429 (2015), 1347-1369. https://doi.org/10.1016/j.jmaa.2015.04.032
13. T. N. Bekjan, Noncommutative symmetric Hardy spaces, Inter. Equat. Oper. Th. 81 (2015), 191-212. https://doi.org/10.1007/s00020-014-2201-6
14. A. Adurexit and T. N. Bekjan, Noncommutative Orlicz-Hardy spaces, Acta Math. Sinica 34B (2014), 1584-1592. https://doi.org/10.1016/S0252-9602(14)60105-3
15. A. Adurexit and T. N. Bekjan, Noncommutative Orlicz-Hardy spaces associated with growth functions, J. Math. Anal. Appl 420 (2014), 824-834. https://doi.org/10.1016/j.jmaa.2014.06.018
16. T. N. Bekjan and Z. Chen, Interpolation and-moment inequalities of noncommutative martingales, Probab. Theory Relat. Fields 152 (2012), 179-206. https://doi.org/10.1007/s00440-010-0319-2
17. T. N. Bekjan, Z. Chen, P. Liu, Y. Jiao, Noncommutative weak Orlicz spaces and martingale inequalities, Studia Math. 204(3) (2011), 195-212. https://doi.org/10.4064/sm204-3-1
18. T. N. Bekjan, Z. Chen, M. Perrin, and Z. Yin, Atomic decomposition and interpolation for Hardy spaces of noncommutative martingales, J. Funct. Anal. 258 (2010), 2483-2505. https://doi.org/10.1016/j.jfa.2009.12.006
19. T. N. Bekjan, -inequalities of noncommutative martingales, Rocky Mountain J. Math. 36 (2) (2006), 401-412. http://www.jstor.org/stable/44239119
Madi Raikhan, Chief Researcher, holds a degree in Mathematics, Candidate of Physical and Mathematical Sciences.
h-index: 2 (Scopus: https://www.scopus.com/authid/detail.uri?authorId=55945027400 ).
Research interests: operator theory, operator algebras, functional analysis. He has published 20 scientific papers, including 10 in the project area. He has served as a scientific supervisor of grant-funded research projects during 2018–2023.
Key publications related to the project area:
1. T. N. Bekjan, Madi Raikhan, On noncommutative weak Orlicz-Hardy spaces, Ann. Funct. Anal. 13, 7(2022). https://doi.org/10.1007/s43034-021-00150-9
2. T. N. Bekjan, Zeqian Chen, Madi Raikhan and Mu Sun, Interpolation and the John-nirenberg inequality on symmetric spaces of noncommutative martingales, Studia Mathematica, 262(3) (2022), 241-273. https://doi.org/10.4064/sm200508-11-12
3. R. Ahat, M. Raikhan, Submajorization inequalities for matrices of ¦У-measurable operators, Linear and Multilinear Algebrathis (2020), https://doi.org/10.1080/03081087.2020.1828248
4. T. N. Bekjan, Madi Raikhan, A Beurling-Blecher-Labuschagne type theorem for Haagerup noncommutative spaces, Banach J. Math. Anal. 15, 39 (2021).https://doi.org/10.1007/s43037-021-00121-1
5. T. N. Bekjan, Madi Raikhan, Interpolation of Haagerup noncommutative Hardy spaces, Banach J. Math. Anal. 13 (2019), no. 4, 798-814. https://doi.org/10.1215/17358787-2018-0026
6. K.S. Tulenov and M. Raikhan, Outer operators for the noncommutative symmetric Hardy spaces with finite subdiagonal algebras, Acta Mathematica Scientia 37(3) (2017), 799-805. https://doi.org/10.1016/S0252-9602(17)30038-3
7. S. Junis and M. Raikhan, A-invariant subspaces of noncommutative Orlicz spaces, J. Xinjiang Univ. Nat. Sci. 33(3) (2016), 301-306.
8. T. N. Bekjan and Madi Raikhan, An Hadamard-type inequality, Linear Algebra and Applications 443 (2014), 228-234. https://doi.org/10.1016/j.laa.2013.11.019
9. N. Biyarov and M. Raikhan, Nonselfadjoint correct restrictions and extensions with the real spectrum, AIP Conference Proceedings 1611, 138 (2014). https://doi.org/10.1063/1.4893818
Dauitbek Dostilek, Leading Researcher, PhD, with over 10 years of experience in the project field.
He has published more than 20 original scientific papers, including 8 related to the project area. He has experience both as a project leader and as a research team member. He led a grant-funded project for young scientists during 2021–2023.
1. D. Dauitbek and K. Tulenov. Conditional expectation on non-commutative, $H_p^{(r,s)}(\A;\ell_\8)$ and $H_p(\A;\ell_1)$ spaces: semifinite case, Ann. Funct. Anal. 11(3) (2020), 617-625. https://doi.org/10.1007/s43034-019-00042-z
2. D. Dauitbek, J. Huang and F. Sukochev, Extreme points of the set of elements majorised by an integrablefunction: Resolution of a problem by Luxemburg, Advances in Mathematics 365 (2020) , No. 107050, 1-27. http://dx.doi.org/10.1016/j.aim.2020.107050
3. D. Dauitbek, Submajorization inequalities for measurable operators, AIP Conference Proceedings 1676, No. 020039 (2015), 1-5. https://doi.org/10.1063/1.4930465
4. T. N. Bekjan, D. Dauitbek, Submajorization inequalities of $\tau$-measurable operators for concave and convex functions, Positivity 19 (2) (2015), 341-345. https://doi.org/10.1007/s11117-014-0300-x
5. T. N. Bekjan, K. Tulenov and D. Dauitbek, The noncommutative $H^{(r,s)}_{p}(\A;\ell_{\infty})$ and $H_{p}(\A;\ell_{1})$ spaces, Positivity 19(4) (2015), 877-891. https://doi.org/10.1007/s11117-015-0332-x
6. D. Dauitbek, N. E. Tokmagambetov and K. S. Tulenov, Commutator inequalities associated with polar decompositions of $\tau$-measurable operators, Russian Math. (Iz. VUZ) 58 (7) (2014), 48-52. https://doi.org/10.3103/S1066369X14070056
7. T. N. Bekjan and Dostilek Dauitbek, Submajorization inequalities of measurable operators, AIP Conference Proceedings 1611, 145 (2014); https://doi.org/10.1063/1.4893820
8. Dauitbek, A. M. Tleulessova , Non-commutative Clarkson inequalities for symmetric space norm of $\tau$-measurable operators, Int. Journal of Math. Analysis 7(18) (2013), 883-890. http://dx.doi.org/10.12988/ijma.2013.13085
Maktagul Alday, Senior Researcher, Candidate of Physical and Mathematical Sciences.
She has published more than 20 original scientific papers and has experience working as a researcher in scientific projects.
1. M. Alday, A.I. Ibatov, Z.S. Aldiyarova, Methods for solving basic equations of Mathematical physics, L. N. Gumilyov ENU, 2020. P. 212
2. M. Alday, K.R. Myrzataeva, Introduction to ordinary differential equations, L. N. Gumilyov ENU, 2018. P. 212
3. M. Alday, K.R. Myrzataeva, A. Eskermesuly, Oscillatory properties of a Class of Fourth-Order Differential Equation, ENU Habarshy 6 (121) (2017), 5-13.
4. M. Alday, Bayarystanov A.O., Ramazanova K.S. Focuslessness conditions for one class of second-order semilinear differential equations on a given interval, ENU Habarshy 6(109) (2015), 5-11.
Azhar Uatayeva (Oshanova), Junior Researcher, early-career scientist, PhD doctoral student.
She has published two scientific papers in the project area and possesses sufficient expertise in the project topic. She participated in the implementation of three grant-funded research projects during 2017–2021.
Key publications related to the project area:
1. S. Junis and A. Oshanova, On submajorization inequalities for matrices of measurable operators, DOI: 10.1007/s43036-020-00101-6, to appear in Advances in Operator Theory.
2. T. N. Bekjan and A. Oshanova, Semifinite tracial subalgebras, Annals of Functional Analysis, 8(4) (2017), 473–478. http://doi.org/10.1215/20088752-2017-0011
Aidana Zhalgas, Junior Researcher, early-career scientist. Author of more than two original scientific publications and has experience as a research project participant.
Tolkynai Elemes, Junior Researcher, early-career scientist. Author of more than two original scientific publications and has experience in research project implementation.
Zhuldyz Sotsial, Junior Researcher, early-career scientist. Author of more than two original scientific publications and has experience as a research project participant.