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Bikchentaev, Airat Midkhatovich
Statistics
Total publications: 59
Scientific articles: 56
Presentations: 11
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
2026
1. A. M. Bikchentaev, “Hyponormal measurable operators affiliated with a semifinite von Neumann algebra. IV”, Sibirsk. Mat. Zh., 67:1 (2026),  15–23  mathnet; Siberian Math. J., 67:1 (2026), 10–17
2025
2. 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 1
3. 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 1
2024
4. 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 2
5. 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
6. 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
7. 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 4
8. 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
9. 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
10. 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 9
2021
11. 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
12. 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
13. 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
14. 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 10
2019
15. 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
16. 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
17. 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
18. 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
19. 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
20. 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
21. 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
22. 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
23. 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
24. 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
25. 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
26. 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
27. 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
28. 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
29. 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
30. 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
31. 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
32. 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
33. 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 25
34. 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
35. 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
36. 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 29
37. 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
38. 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
39. 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
40. 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
41. 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
42. 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
43. 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
44. 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
45. 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
46. 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
47. 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
48. 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
49. 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
50. 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 26
1998
51. 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
52. 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
53. A. M. Bikchentaev, “A connection between random and fuzzy metrics. II”, Konstr. Teor. Funkts. Funkts. Anal., 6 (1987),  58–61  mathnet  mathscinet  zmath
1985
54. A. M. Bikchentaev, “A connection between random and fuzzy metrics”, Konstr. Teor. Funkts. Funkts. Anal., 5 (1985),  3–15  mathnet  mathscinet  zmath 1
2021
55. 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
56. 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
57. 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. О гипонормальных измеримых операторах
A. M. Bikchentaev
International scientific conference “Infinite-dimensional analysis and mathematical physics” (IDAMPh 2026)
January 26, 2026 14:30   
2. 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   
3. 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
4. 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
5. 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   
6. Коммутаторы измеримых операторов, имеющие нулевые следы
A. M. Bikchentaev

May 22, 2024 14:30   
7. 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   
8. Commutators in C*-algebras and traces
A. M. Bikchentaev
International Conference "New Trends in Mathematical Physics"
November 12, 2022 11:00   
9. 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   
10. 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   
11. 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

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