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Bikchentaev, Airat Midkhatovich
Bikchentaev, Airat Midkhatovich
Associate professor
Doctor of physico-mathematical sciences (2012)
Speciality: 01.01.01 (Real analysis, complex analysis, and functional analysis)
Birth date: 28.04.1960
E-mail:
Keywords: quantum logics, fuzzy sets, von Neumann algebra, Hilbert space, trace, weight, projection, measurable operator, noncommutative integration, measure topology.
UDC: 517.98, 517.983, 517.986, 517.987

Subject:

Operator theory, noncommutative integration.
   
Main publications:
  • Amer. Math. Soc. Transl. Ser. 2, 1992.
  • Intern. J. Theor. Physics, V. 37(1998), no. 1, 571–576.
  • Dokl. RAN, Tom 393 (2003), no. 4, 444–447.
  • Matematicheskie zametki, T. 64 (1998), no. 2, 185–190; T. 75 (2004), no. 3, 342–349; T. 76 (2004), no. 3, 625–628; T. 79 (2006), no. 2, 311–315; T. 82 (2007), no. 5, 783–786.
  • Sibirskii matem. zhurn., 46 (2005), no. 1, 32–45.
  • Matematicheskii sbornik, 2008.
  • Tr. Matem. in-ta im. V. A. Steklova, T. 255 (2006), 41–54.

https://www.mathnet.ru/eng/person18192
List of publications on Google Scholar
https://mathscinet.ams.org/mathscinet/MRAuthorID/230625
https://orcid.org/0000-0001-5992-3641

Publications in Math-Net.Ru Citations
2025
1. A. M. Bikchentaev, “Trace inequalities for measurable operators affiliated to a von Neumann algebra”, Izv. Vyssh. Uchebn. Zaved. Mat., 2025, no. 1,  99–104  mathnet; Russian Math. (Iz. VUZ), 69:1 (2025), 90–95
2. A. M. Bikchentaev, “Hyponormal measurable operators affiliated to a semifinite von Neumann algebra”, Sibirsk. Mat. Zh., 66:3 (2025),  396–405  mathnet; Siberian Math. J., 66:3 (2025), 656–663
2024
3. A. M. Bikchentaev, “The trace and integrable commutators of the measurable operators affiliated to a semifinite von Neumann algebra”, Sibirsk. Mat. Zh., 65:3 (2024),  455–468  mathnet; Siberian Math. J., 65:3 (2024), 522–533 1
4. A. M. Bikchentaev, O. E. Tikhonov, “Continuity of Operator Functions in the Topology of Local Convergence in Measure”, Trudy Mat. Inst. Steklova, 324 (2024),  51–59  mathnet  mathscinet  zmath; Proc. Steklov Inst. Math., 324 (2024), 44–52  scopus 1
5. G. G. Amosov, A. M. Bikchentaev, V. Zh. Sakbaev, “On Extreme Points of Sets in Operator Spaces and State Spaces”, Trudy Mat. Inst. Steklova, 324 (2024),  10–23  mathnet  mathscinet  zmath; Proc. Steklov Inst. Math., 324 (2024), 4–17  scopus 2
2023
6. A. M. Bikchentaev, “A block projection operator in the algebra of measurable operators”, Izv. Vyssh. Uchebn. Zaved. Mat., 2023, no. 10,  77–82  mathnet; Russian Math. (Iz. VUZ), 67:10 (2023), 70–74 3
7. A. M. Bikchentaev, “The topologies of local convergence in measure on the algebras of measurable operators”, Sibirsk. Mat. Zh., 64:1 (2023),  17–27  mathnet  mathscinet; Siberian Math. J., 64:1 (2023), 13–21 3
2022
8. A. M. Bikchentaev, “Invertibility of the Operators on Hilbert Spaces and Ideals in $C^*$-Algebras”, Mat. Zametki, 112:3 (2022),  350–359  mathnet  mathscinet; Math. Notes, 112:3 (2022), 360–368  scopus 1
9. A. M. Bikchentaev, “Essentially invertible measurable operators affiliated to a semifinite von Neumann algebra and commutators”, Sibirsk. Mat. Zh., 63:2 (2022),  272–282  mathnet; Siberian Math. J., 63:2 (2022), 224–232 8
2021
10. A. M. Bikchentaev, Kh. Fawwaz, “Differences and commutators of idempotents in $C^*$-algebras”, Izv. Vyssh. Uchebn. Zaved. Mat., 2021, no. 8,  16–26  mathnet; Russian Math. (Iz. VUZ), 65:8 (2021), 13–22 7
2020
11. A. M. Bikchentaev, “Convergence in measure and $\tau$-compactness of $\tau$-measurable operators, affiliated with a semifinite von Neumann algebra”, Izv. Vyssh. Uchebn. Zaved. Mat., 2020, no. 5,  89–93  mathnet; Russian Math. (Iz. VUZ), 64:5 (2020), 79–82  isi  scopus 3
12. A. M. Bikchentaev, “Seminorms Associated with Subadditive Weights on $C^*$-Algebras”, Mat. Zametki, 107:3 (2020),  341–350  mathnet  mathscinet  elib; Math. Notes, 107:3 (2020), 383–391  isi  scopus 3
13. A. M. Bikchentaev, “Inequalities for determinants and characterization of the trace”, Sibirsk. Mat. Zh., 61:2 (2020),  314–321  mathnet  elib; Siberian Math. J., 61:2 (2020), 248–254  isi  scopus 9
2019
14. A. M. Bikchentaev, “Ideal $F$-norms on $C^*$-algebras. II”, Izv. Vyssh. Uchebn. Zaved. Mat., 2019, no. 3,  90–96  mathnet; Russian Math. (Iz. VUZ), 63:3 (2019), 78–82  isi  scopus 4
15. A. M. Bikchentaev, “Trace and Differences of Idempotents in $C^*$-Algebras”, Mat. Zametki, 105:5 (2019),  647–655  mathnet  mathscinet  elib; Math. Notes, 105:5 (2019), 641–648  isi  scopus 15
16. A. M. Bikchentaev, “Metrics on projections of the von neumann algebra associated with tracial functionals”, Sibirsk. Mat. Zh., 60:6 (2019),  1223–1228  mathnet  elib; Siberian Math. J., 60:6 (2019), 952–956  isi  scopus 6
17. A. M. Bikchentaev, “Renormalizations of measurable operator ideal spaces affiliated to semi-finite von Neumann algebra”, Ufimsk. Mat. Zh., 11:3 (2019),  3–9  mathnet; Ufa Math. J., 11:3 (2019), 3–10  isi  scopus 4
2018
18. A. M. Bikchentaev, “Trace and Commutators of Measurable Operators Affiliated to a von Neumann Algebra”, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 151 (2018),  10–20  mathnet  mathscinet; J. Math. Sci. (N. Y.), 252:1 (2021), 8–19 2
19. A. M. Bikchentaev, S. A. Abed, “Paranormal elements in normed algebra”, Izv. Vyssh. Uchebn. Zaved. Mat., 2018, no. 5,  13–19  mathnet; Russian Math. (Iz. VUZ), 62:5 (2018), 10–15  isi  scopus 2
20. A. M. Bikchentaev, “Ideal spaces of measurable operators affiliated to a semifinite von Neumann algebra”, Sibirsk. Mat. Zh., 59:2 (2018),  309–320  mathnet  elib; Siberian Math. J., 59:2 (2018), 243–251  isi  scopus 8
21. A. M. Bikchentaev, “Differences of idempotents in $C^*$-algebras and the quantum Hall effect”, TMF, 195:1 (2018),  75–80  mathnet  mathscinet  elib; Theoret. and Math. Phys., 195:1 (2018), 557–562  isi  scopus 17
22. A. M. Bikchentaev, “On an analog of the M. G. Krein theorem for measurable operators”, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 160:2 (2018),  243–249  mathnet  isi 1
2017
23. A. M. Bikchentaev, “On the $\tau$-compactness of products of $\tau$-measurable operators adjoint to semi-finite von Neumann algebras”, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 140 (2017),  78–87  mathnet  mathscinet  zmath; Journal of Mathematical Sciences, 241:4 (2019), 458–468 3
24. A. M. Bikchentaev, “Two classes of $\tau$-measurable operators affiliated with a von Neumann algebra”, Izv. Vyssh. Uchebn. Zaved. Mat., 2017, no. 1,  86–91  mathnet; Russian Math. (Iz. VUZ), 61:1 (2017), 76–80  isi  scopus 6
25. A. M. Bikchentaev, “Differences of idempotents in $C^*$-algebras”, Sibirsk. Mat. Zh., 58:2 (2017),  243–250  mathnet  elib; Siberian Math. J., 58:2 (2017), 183–189  isi  elib  scopus 19
2016
26. A. M. Bikchentaev, “On operator monotone and operator convex functions”, Izv. Vyssh. Uchebn. Zaved. Mat., 2016, no. 5,  70–74  mathnet; Russian Math. (Iz. VUZ), 60:5 (2016), 61–65  isi  scopus 9
27. A. M. Bikchentaev, “On Idempotent $\tau$-Measurable Operators Affiliated to a von Neumann Algebra”, Mat. Zametki, 100:4 (2016),  492–503  mathnet  mathscinet  elib; Math. Notes, 100:4 (2016), 515–525  isi  scopus 24
28. A. M. Bikchentaev, “Inequality for a Trace on a Unital $C^*$-Algebra”, Mat. Zametki, 99:4 (2016),  483–488  mathnet  mathscinet  elib; Math. Notes, 99:4 (2016), 487–491  isi  scopus 11
29. A. M. Bikchentaev, “Convergence of integrable operators affiliated to a finite von Neumann algebra”, Trudy Mat. Inst. Steklova, 293 (2016),  73–82  mathnet  mathscinet  elib; Proc. Steklov Inst. Math., 293 (2016), 67–76  isi  scopus 9
2015
30. A. M. Bikchentaev, “Ideal $F$-norms on $C^*$-algebras”, Izv. Vyssh. Uchebn. Zaved. Mat., 2015, no. 5,  69–74  mathnet; Russian Math. (Iz. VUZ), 59:5 (2015), 58–63  scopus 6
31. A. M. Bikchentaev, “Concerning the Theory of $\tau$-Measurable Operators Affiliated to a Semifinite von Neumann Algebra”, Mat. Zametki, 98:3 (2015),  337–348  mathnet  mathscinet  elib; Math. Notes, 98:3 (2015), 382–391  isi  scopus 19
2014
32. A. M. Bikchentaev, “On Normal $\tau$-Measurable Operators Affiliated with Semifinite Von Neumann Algebras”, Mat. Zametki, 96:3 (2014),  350–360  mathnet  mathscinet  zmath  elib; Math. Notes, 96:3 (2014), 332–341  isi  elib  scopus 24
33. A. M. Bikchentaev, “On additivity of mappings on measurable functions”, Sibirsk. Mat. Zh., 55:1 (2014),  11–16  mathnet  mathscinet; Siberian Math. J., 55:1 (2014), 7–11  isi  scopus 1
2013
34. A. M. Bikchentaev, “The Haagerup problem on subadditive weights on $W^*$-algebras. II”, Izv. Vyssh. Uchebn. Zaved. Mat., 2013, no. 12,  72–76  mathnet; Russian Math. (Iz. VUZ), 57:12 (2013), 66–69  scopus 4
2012
35. A. M. Bikchentaev, “Block projection operators in normed solid spaces of measurable operators”, Izv. Vyssh. Uchebn. Zaved. Mat., 2012, no. 2,  86–91  mathnet  mathscinet; Russian Math. (Iz. VUZ), 56:2 (2012), 75–79  scopus 28
36. A. M. Bikchentaev, A. A. Sabirova, “Dominated convergence in measure on semifinite von Neumann algebras and arithmetic averages of measurable operators”, Sibirsk. Mat. Zh., 53:2 (2012),  258–270  mathnet  mathscinet; Siberian Math. J., 53:2 (2012), 207–216  isi  scopus 5
2011
37. A. M. Bikchentaev, “The Haagerup problem on subadditive weights on $W^*$-algebras”, Izv. Vyssh. Uchebn. Zaved. Mat., 2011, no. 10,  94–98  mathnet  mathscinet; Russian Math. (Iz. VUZ), 55:10 (2011), 82–85  scopus 6
38. A. M. Bikchentaev, “Commutation of Projections and Trace Characterization on von Neumann Algebras. II”, Mat. Zametki, 89:4 (2011),  483–494  mathnet  mathscinet; Math. Notes, 89:4 (2011), 461–471  isi  scopus 24
2010
39. A. M. Bikchentaev, “On a Lemma of Berezin”, Mat. Zametki, 87:5 (2010),  787–791  mathnet  mathscinet; Math. Notes, 87:5 (2010), 768–773  isi  scopus 12
40. A. M. Bikchentaev, “Commutativity of projections and characterization of traces on von Neumann algebras”, Sibirsk. Mat. Zh., 51:6 (2010),  1228–1236  mathnet  mathscinet  elib; Siberian Math. J., 51:6 (2010), 971–977  isi  scopus 25
2009
41. A. M. Bikchentaev, “Commutativity of projectors and trace characterization on von Neumann algebras. I”, Izv. Vyssh. Uchebn. Zaved. Mat., 2009, no. 12,  80–83  mathnet  mathscinet  zmath; Russian Math. (Iz. VUZ), 53:12 (2009), 68–71 4
2008
42. A. M. Bikchentaev, “On the representation of elements of a von Neumann algebra in the form of finite sums of products of projections. III. Commutators in $C^*$-algebras”, Mat. Sb., 199:4 (2008),  3–20  mathnet  mathscinet  zmath  elib; Sb. Math., 199:4 (2008), 477–493  isi  elib  scopus 13
2007
43. A. M. Bikchentaev, “Local Convergence in Measure on Semifinite von Neumann Algebras, II”, Mat. Zametki, 82:5 (2007),  783–786  mathnet  mathscinet  zmath  elib; Math. Notes, 82:5 (2007), 703–707  isi  scopus 11
2006
44. A. M. Bikchentaev, “Projection-Convex Combinations in $C^*$-Algebras and the Invariant Subspace Problem, I”, Mat. Zametki, 79:2 (2006),  311–315  mathnet  mathscinet  zmath  elib; Math. Notes, 79:2 (2006), 285–290  isi  scopus 5
45. A. M. Bikchentaev, “Local Convergence in Measure on Semifinite von Neumann Algebras”, Trudy Mat. Inst. Steklova, 255 (2006),  41–54  mathnet  mathscinet  elib; Proc. Steklov Inst. Math., 255 (2006), 35–48  scopus 17
2005
46. A. M. Bikchentaev, “On representation of elements of a Von Neumann algebra in the form of finite sums of products of projections”, Sibirsk. Mat. Zh., 46:1 (2005),  32–45  mathnet  mathscinet  zmath; Siberian Math. J., 46:1 (2005), 24–34  isi 20
2004
47. A. M. Bikchentaev, “The continuity of multiplication for two topologies associated with a Semifinite trace on von Neumann algebra”, Lobachevskii J. Math., 14 (2004),  17–24  mathnet  mathscinet  zmath 6
48. A. M. Bikchentaev, A. N. Sherstnev, “Projective Convex Combinations in $C^*$-Algebras with the Unitary Factorization Property”, Mat. Zametki, 76:4 (2004),  625–628  mathnet  mathscinet  zmath; Math. Notes, 76:4 (2004), 578–581  isi  scopus 8
49. A. M. Bikchentaev, “Minimality of Convergence in Measure Topologies on Finite von Neumann Algebras”, Mat. Zametki, 75:3 (2004),  342–349  mathnet  mathscinet  zmath; Math. Notes, 75:3 (2004), 315–321  isi 25
1998
50. A. M. Bikchentaev, “On a property of $L_p$ spaces on semifinite von Neumann algebras”, Mat. Zametki, 64:2 (1998),  185–190  mathnet  mathscinet  zmath; Math. Notes, 64:2 (1998), 159–163  isi 39
1992
51. A. M. Bikchentaev, “The triangle inequality for some spaces of measurable operators”, Konstr. Teor. Funkts. Funkts. Anal., 8 (1992),  23–32  mathnet  mathscinet  zmath 1
1987
52. A. M. Bikchentaev, “A connection between random and fuzzy metrics. II”, Konstr. Teor. Funkts. Funkts. Anal., 6 (1987),  58–61  mathnet  mathscinet  zmath
1985
53. A. M. Bikchentaev, “A connection between random and fuzzy metrics”, Konstr. Teor. Funkts. Funkts. Anal., 5 (1985),  3–15  mathnet  mathscinet  zmath 1
2021
54. N. R. Abubakirov, F. G. Avkhadiev, A. V. Aminova, M. M. Arslanov, A. M. Bikchentaev, V. V. Vasin, F. N. Garif'yanov, A. M. Denisov, A. M. Elizarov, N. K. Zamov, B. A. Kats, O. A. Kashina, D. V. Maklakov, V. P. Maksimov, S. R. Nasyrov, N. I. Popov, L. G. Salekhov, R. B. Salimov, S. G. Samko, N. Temirgaliev, E. A. Turilova, Yu. E. Hohlov, P. L. Shabalin, L. N. Shevrin, A. N. Sherstnev, E. A. Shirokova, V. V. Shurygin, “Leonid Aleksandrovich Aksent'ev”, Izv. Vyssh. Uchebn. Zaved. Mat., 2021, no. 3,  98–100  mathnet
2018
55. L. A. Aksent'ev, A. I. Aptekarev, A. M. Bikchentaev, V. V. Goryainov, V. N. Dubinin, A. M. Elizarov, I. R. Kayumov, A. Laptev, S. R. Nasyrov, D. V. Prokhorov, A. G. Sergeev, V. D. Stepanov, “Farit Gabidinovich Avkhadiev (on his 70th birthday)”, Uspekhi Mat. Nauk, 73:1(439) (2018),  187–190  mathnet  mathscinet  zmath  elib; Russian Math. Surveys, 73:1 (2018), 181–185  isi
56. A. M. Bikchentaev, S. R. Nasyrov, E. A. Turilova, “Anatolij Nikolaevich Sherstnev (on 80th birthday anniversary)”, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 160:3 (2018),  590–598  mathnet

Presentations in Math-Net.Ru
1. Данияр Хамидович Муштари: ученый, педагог, человек. К 80-летию со дня рождения
A. M. Bikchentaev
XVII International Kazan school-conference "Function Theory, Its Applications and Related Topics"
August 24, 2025   
2. On spaces of measurable operators
A. M. Bikchentaev
International conference "Theory of functions and its applications" dedicated to the 120th anniversary of S. M. Nikol'skii
July 5, 2025 15:45
3. О гипонормальных измеримых операторах, присоединенных к полуконечной алгебре фон Неймана
A. M. Bikchentaev
International scientific conference “Infinite-dimensional analysis and mathematical physics” (IDAMPh 2025)
January 27, 2025 10:30
4. О классах симметричных и асимметричных логик множеств
A. M. Bikchentaev, M. Mohamed Ali, Kh. Fawwaz
International conference “Theory of Functions, Operator Theory and Quantum Information Theory”
June 11, 2024 16:50   
5. Коммутаторы измеримых операторов, имеющие нулевые следы
A. M. Bikchentaev

May 22, 2024 14:30   
6. Commutators in C*-algebras and traces
A. M. Bikchentaev
III International Conference “Mathematical Physics, Dynamical Systems, Infinite-Dimensional Analysis”, dedicated to the 100th anniversary of V.S. Vladimirov, the 100th anniversary of L.D. Kudryavtsev and the 85th anniversary of O.G. Smolyanov
July 7, 2023 15:00   
7. Commutators in C*-algebras and traces
A. M. Bikchentaev
International Conference "New Trends in Mathematical Physics"
November 12, 2022 11:00   
8. Квантовые состояния и меры на единичной сфере гильбертова пространства
G. G. Amosov, V. Zh. Sakbaev, A. M. Bikchentaev
Infinite dimensional analysis and mathematical physics
October 24, 2022 18:30   
9. The algebra of thin $\tau$-measurable operators is directly finite
A. M. Bikchentaev
Complex Analysis and Related Topics (satelllite of ICM-2022)
July 1, 2022 17:20   
10. О $\tau$-измеримых операторах, присоединенных к полуконечной алгебре фон Неймана
A. M. Bikchentaev
International conference on Function Spaces and Approximation Theory dedicated to the 110th anniversary of S. M. Nikol'skii
May 29, 2015 17:05

Organisations