01.01.01 (Real analysis, complex analysis, and functional analysis)
E-mail:
Main publications:
A. F. Ber,
K. K. Kudaybergenov,
F. A. Sukochev, “Derivations of Murray–von Neumann algebras”, Journal für die reine und angewandte Mathematik (Crelles Journal), 791:10 (2022), 283–301
Sh. A. Ayupov, K. K. Kudaybergenov, “Ring isomorphisms of Murray–von Neumann algebras”, Journal of Functional Analysis, 280:5 (2021), 108891
Sh. A. Ayupov, A. Elduque, K. K. Kudaybergenov, “Local derivations and automorphisms of Cayley algebras”, Journal of Pure and Applied Algebra, 227:5 (2023), Paper No. 107277
S. Albeverio, Sh. A. Ayupov, K. K. Kudaybergenov, “Structure of derivations on various algebras of measurable operators for type I von Neumann algebras”, Journal of Functional Analysis, 256:9 (2009), 2917–2943
S. Albeverio, Sh. A. Ayupov, K. K. Kudaybergenov, “Non-commutative Arens algebras and their derivations”, Journal of Functional Analysis, 253:1 (2007), 287–302
S. Albeverio, Sh. A. Ayupov, K. K. Kudaybergenov, “Structure of derivations on various algebras of measurable operators for type I von Neumann algebras”, Journal of Functional Analysis, 256:9 (2009), 2917-2943
Sh. A. Ayupov, K. K. Kudaybergenov, “2-Local derivations and automorphisms on $B(H)$”, Journal of Mathematical Analysis and Applications, 395:1 (2012), 15–18
Sh. A. Ayupov, K. K. Kudaybergenov,B. O. Nurjanov, A. K. Alauadinov, “Local and 2-local derivations on noncommutative Arens algebras”, Mathematica Slovaca, 2014, 423-432
S. Albeverio, Sh. A. Ayupov, K. K. Kudaybergenov, “Non-commutative Arens algebras and their derivations”, Journal of Functional Analysis, 253:1 (2007), 287–302
Sh. A. Ayupov, K. K. Kudaybergenov, B. Yusupov, “2-Local derivations on generalized Witt algebras”, Linear and Multilinear Algebra, 69:16 (2021), 3130-3140
Sh. A. Ayupov, K. K. Kudaybergenov, “Derivations on algebras of measurable operators”, Infinite Dimensional Analysis, Quantum Probability and Related Topics, 2010 , 305-337 pp.
S. Albeverio, Sh. A. Ayupov, K. K. Kudaybergenov, “Derivations on the algebra of measurable operators affiliated with a type I von Neumann algebra”, Siberian Advances in Mathematics, 18 (2008)
Sh. A. Ayupov, A. Elduque, K. K. Kudaybergenov, “Local derivations and automorphisms of Cayley algebras”, Journal of Pure and Applied Algebra, 227:5 (2023), Paper No. 107277
Sh. A. Ayupov, K. K. Kudaybergenov, A. K. Alauadinov, “2-Local derivations on matrix algebras over commutative regular algebras”, Linear Algebra and its Applications, 439:5 (2013), 1294–1311
Sh. A. Ayupov, K. K. Kudaybergenov, “Innerness of continuous derivations on algebras of measurable operators affiliated with finite von Neumann algebras”, Journal of Mathematical Analysis and Applications, 408 (2013), 256–267
A. F. Ber, K. K. Kudaybergenov, F. A. Sukochev, “Notes on derivations of Murray–von Neumann algebras”, Journal of Functional Analysis, 279:5 (2020), 108
A. F. Ber, K. K. Kudaybergenov, F. A. Sukochev, “Derivations on Murray–von Neumann algebras”, Russian Math. Surveys, 74:5 (2019), 950–952
18.
V. I. Chilin, I. G. Ganiev, K. K. Kudaibergenov, “GNS-representations of $C^*$-algebras over the ring of measurable function”, Vladikavkaz. Mat. Zh., 9:2 (2007), 33–39
19.
B. L. Macedo Ferreira, I. Kaygorodov, K.K. Kudaybergenov, “Local and 2-local derivations of simple n-ary algebras”, Ricerche di Matematica, 73:1 (2024), 341-350
K. K. Kudaybergenov, B. A. Omirov, T. K.Kurbanbaev, “Local derivations on solvable Lie algebras of maximal rank”, Communications in Algebra, 50:9 (2022), 3816-3826
Sh. A. Ayupov, K. K. Kudaybergenov, “Infinite dimensional central simple regular algebras with outer derivations”, Lobachevskii Journal of Mathematics, 41 (2020), 326-332
Sh. A. Ayupov, K. K. Kudaybergenov, B. Yusupov, “Local and 2-local derivations of $p$-filiform Leibniz algebras”, Journal of Mathematical Sciences, 245 (2020), 359–367
Sh. A. Ayupov, K. K. Kudaybergenov, B. B. Yusupov, “Local and $2$-Local Differentiations of $p$-Filiform Leibniz Algebras”, Journal of Mathematical Sciences, 245:3 (2020), 359–367
25.
M. M. Ibragimov, K. K. Kudaibergenov, “Geometric description of $L_1$-spaces”, Russian Math. (Iz. VUZ), 57:9 (2013), 16–21
26.
M. M. Ubragimov, K. K. Kudaybergenov, S. Zh. Tleumuratov, Zh. Kh. Sejpullaev, “Geometric description of the preduals of atomic commutative von Neumann algebras”, Math. Notes, 93:5 (2013), 715–721
27.
V. I. Chilin, I. G. Ganiev, K. K. Kudaibergenov, “The Gel'fand-Naĭmark theorem for $C^*$-algebras over a ring of measurable functions”, Russian Math. (Iz. VUZ), 52:2 (2008), 58–66
28.
I. G. Ganiev, K. K. Kudaǐbergenov, “Banach's theorem on an inverse operator in Banach-Kantorovich spaces”, Vladikavkaz. Mat. Zh., 6:3 (2004), 21–25
29.
Sh. A. Ayupov, K. K. Kudaybergenov, A. Allambergenov, “Local and 2-local derivations on octonion algebras”, Journal of algebra and its applications, 22:7 (2023), Paper No 2350147 , 12 pp.
K. K. Kudaybergenov, B. O. Nurjanov, “Partial orders on $\ast$-regular rings”, Ufa Math. J., 15:1 (2023), 34–42
31.
M. M. Ibragimov, K. K. Kudaibergenov, Zh. Kh. Seipullaev, “Facially symmetric spaces and predual ones of Hermitian part of von Neumann algebras”, Russian Math. (Iz. VUZ), 62:5 (2018), 27–33
32.
J. Hamhalter, K. K. Kudaybergenov, A. M. Peralta, B. Russo, “Boundedness of completely additive measures with application to 2-local triple derivations”, Journal of Mathematical Physics, 57 (2016), 021709
K. K. Kudaybergenov, F. M. Mukhamedov, “Spectral decomposition of self-adjoint cyclically compact operators and partial integral equations”, Acta Mathematica Hungarica, 149 (2016), 297–305
S. Albeverio, Sh. A. Ayupov, K. K. Kudaybergenov, “Derivations on the algebra of $\tau$-compact operators affiliated with a type I von Neumann algebra”, Positivity, 12 (2008), 375–386
Sh. A. Ayupov, K. K. Kudaibergenov, “Derivations of Noncommutative Arens Algebras”, Funct. Anal. Appl., 41:4 (2007), 303–305
36.
Sh. A. Ayupov, K. K. Kudaybergenov, B. Yusupov, “Local and 2-local derivations of locally simple Lie algebras”, Journal of Mathematical Sciences, 278 (2024), 613-622
J. Huang, K. K. Kudaybergenov, F. A. Sukochev, “Ring derivations of Murray–von Neumann algebras”, Linear algebra and its applications, 672:1 (2023) , 28-52 pp.
Sh. A. Ayupov, K. K. Kudaybergenov, B. Yusupov, “Lokalnye i 2-lokalnye differentsirovaniya lokalno prostykh algebr Li”, Sovremennaya matematika. Fundamentalnye napravleniya, 68:1 (2022), 59-69
Sh. A. Ayupov, K. K. Kudaybergenov, “Ring isomorphisms of *-subalgebras of Murray–von Neumann factors”, Lobachevskii Journal of Mathematics, 42:12 (2021), 2730-2739
I. G. Ganiev, K. K. Kudaibergenov, “The Banach–Steinhaus uniform boundedness principle for operators in Banach–Kantorovich spaces over $L^0$”, Siberian Adv. Math., 16:3 (2006), 42–53
43.
K. K. Kudaybergenov, B. A. Omirov, T. K. Kurbanbaev, “Local automorphisms of complex solvable Lie algebras of maximal rank”, Linear and Multilinear Algebra, 72:13 (2024), 2197-2220
A. F. Ber, J. Huang, K. K. Kudaybergenov, F. A. Sukochev, “Non-existence of translation-invariant derivations on algebras of measurable functions”, Quaestiones Mathematicae, 46:5 (2023), 905-926
A. D. Arziev, K. K. Kudaybergenov, P. R. Oriinbaev, A. K. Tangirbergen, “Partial Integral Operators on Banach–Kantorovich Spaces”, Math. Notes, 114:1 (2023), 15–29
46.
K. K. Kudaybergenov, A. D. Arziev, “The spectrum of an element in a Banach-Kantorovich algebra over a ring of measurable functions”, Advances in Operator Theory, 2022, no. 7, 1-15
K. K. Kudaybergenov, J. Kh. Seypullaev, “Characterization of JBW-algebras with strongly facially symmetric predual space”, Math. Notes, 107:4 (2020), 600–608
48.
Sh. A. Ayupov, K. K. Kudaybergenov, “Local derivations on measurable operators and commutativity”, European Journal of Mathematics, 2 (2016) , 8 pp.
Sh. A. Ayupov, R. Z. Abdullaev, K. K. Kudaybergenov, “On a certain class of operator algebras and their derivations”, Eurasian Math. J., 5:1 (2014), 82–94
K. K. Kudaybergenov, K. U. Begjanova, “Description of weakly additive order-preserving functionals on the plane”, Vladikavkaz. Mat. Zh., 13:1 (2011), 31–37
51.
Sh. A. Ayupov, K. K. Kudaybergenov, “Innerness of derivations on subalgebras of measurable operators”, Lobachevskii Journal of Mathematics, 29 (2008), 60-67
Sh. A. Ayupov, J. Huang, K. K. Kudaybergenov, “Schur inequality for Murray–von Neumann algebras and its applications”, Annals of Functional Analysis, 15:3 (2024), 24 (article number 47)
53.
J. Huang, K. K. Kudaybergenov, R. Liu, “The ball-covering property of noncommutative symmetric spaces”, Studia Mathematica, 277:2 (2024), 169-190
54.
Sh. A. Ayupov, K. K. Kudaybergenov, “Local derivations of classical simple Lie algebras”, In: Albuquerque, H., Brox, J., Martínez, C., Saraiva, P. (eds) Non-Associative Algebras and Related Topics. NAART 2020. Springer Proceedings in Mathematics & Statistics, 427, Springer, Cham., 2023, 3–16
55.
Sh. A. Ayupov, K. K. Kudaibergenov, Kh. K. Karimov, “Izomorfizm mezhdu algebroi izmerimykh funktsii i ee podalgebroi asimptoticheski differentsiruemykh funktsii”, Vladikavk. matem. zhurn., 25:2 (2023), 25-37
56.
Sh. A. Ayupov, K. K. Kudaybergenov, Kh. K. Karimov, “On dimension of the space of derivations on commutative regular algebras”, Journal of Mathematical Sciences, 271:6 (2023), 694-699
57.
K. K. Kudaibergenov, A. D. Arziev, P. R. Orynbaev, A. K. Tanirbergen, “The Mercer‘s theorem for partial integral operators”, Journal of Mathematical Sciences, 271:6 (2023), 749-761
58.
I. Kaygorodov, K. K. Kudaybergenov, I. Yuldashev, “Local derivations of semisimple Leibniz algebras”, Communications in Mathematics, 30:2 (2022) , 12 pp.
59.
K. K. Kudaybergenov, “On solution of Ayupov's problem”, Bulletin of the Institute of Mathematics, 5:3 (2022), 219–233
60.
Sh. A. Ayupov, K. K. Kudaybergenov, A. Allambergenov, “Local and 2-local automorphisms on octonion algebras”, Uzbek Mathematical Journal, 66:2 (2022), 22-34
61.
Sh. A. Ayupov, K. K. Kudaybergenov, B. A. Omirov, “Local and 2-local derivations and automorphisms on simple Leibniz algebras”, Bulletin of the Malaysian Mathematical Sciences Society, 43:3 (2020), 2199–2234
62.
Sh. A. Ayupov, K. K. Kudaybergenov, B. A. Omirov, K. Zhao, “Semisimple Leibniz algebras, their derivations and automorphisms”, Linear and Multilinear Algebra, 68:10 (2020), 2005-2019
63.
K. K. Kudaybergenov, J. X. Seypullaev, “Description of facially symmetric spaes with unitary tripotents”, Siberian Advances in Mathematics, 30:2 (2020), 2 , 117-123 pp.
64.
K. K. Kudaybergenov, “Derivations of Murray-von Neumann algebras”, Modern problems in mathematics (Nukus, 20 may 2020), KarSU, 2020, 40
65.
Sh. A. Ayupov, K. K. Kudaybergenov, T. S. Kalandarov, “2-Local automorphisms on $AW^\ast$-algebras.”, Positivity and Noncommutative Analysis. Trends in Mathematics, Birkhäuser, 2019, 1–13
Sh. A. Ayupov, K. K. Kudaybergenov, “Local automorphisms on finite dimensional Lie and Leibniz algebras”, Algebra, Complex Analysis, and Pluripotential Theory. USUZCAMP 2017. Springer Proceedings in Mathematics & Statistics, vol 264. Springer, Springer, 2018, 31–44
68.
Sh. A. Ayupov, K. K. Kudaybergenov, A. K. Alauadinov, “2-Local derivations on matrix algebras and algebras of measurable operators”, Advances in Operator Theory, 2:4 (2017), 494-505
69.
K. K. Kudaybergenov, F. M. Mukhamedov, “Self-adjoint cyclically compact operators and its application”, Bulletin of the Korean Mathematical Society, 54 (2017), 679-686
70.
Sh. A. Ayupov, K. K. Kudaybergenov, “Derivations, local and 2-local derivations on algebras of measurable operators”, Topics in Functional Analysis and Algebra, Contemporary Mathematics, 672 (2016), 51-72
71.
Sh. A. Ayupov, K. K. Kudaybergenov, “Derivations, local and 2-local derivations on algebras of measurable operators”, Functional Analysis and Algebra. Contemporary Mathematics, 672, eds. Bernard Russo, Asuman Aksoy, Ravshan Ashurov, Shavkat Ayupov, Amer. Math. Soc., Providence, RI, 2016, 51-72
72.
Sh. A. Ayupov, K. K. Kudaybergenov, A. M. Peralta, “A survey on
local and 2-local derivations on $C^*$- and von Neumann algebras”, Topics in Functional Analysis and Algebra. Contemporary Mathematics, eds. Bernard Russo, Asuman Aksoy, Ravshan Ashurov, Shavkat Ayupov, Amer. Math. Soc., Providence, RI, 2016, 73-126
73.
K. K. Kudaybergenov, F. M. Mukhamedov, “Local Derivations on Subalgebras of τ-Measurable Operators with Respect to Semi-finite von Neumann Algebras”, Mediterranean Journal of Mathematics volume, 12 (2015), 1009–1017
74.
K. K. Kudaybergenov, T. Oikhberg, A. M. Peralta, B. Russo, “2-local triple derivations on von Neumann algebras”, Illinois J. Math., 58 (2014), 1055-1069
75.
Sh. A. Ayupov, K. K. Kudaybergenov, “Spatiality of derivations on the algebra of $\tau$-compact operators”, Integral Equations and Operator Theory, 77 (2013), 581-598
76.
N. Yadgorov,M. M. Ibragimov, K. K. Kudaybergenov, “Geometric characterization of $L_1$-spaces”, Studia Mathematica, 219 (2013), 97-107
77.
Sh. A. Ayupov, K. K. Kudaybergenov, A. K. Alauadinov, “2 -local derivations on algebras of locally measurable operators”, Annals of Functional Analysis, 4 (2013), 110-117
78.
Sh. A. Ayupov, K. K. Kudaybergenov, R. Djumamuratov, “Topologies on central extensions of von Neumann algebras”, Central European Journal of Mathematics, 10 (2012), 656-664
79.
S. Albeverio, K. K. Kudaybergenov, R. Djumamuratov, “Conditions of coincidence of central extensions of von Neumann algebras and algebras of measurable operators”, Lobachevskii Journal of Mathematics, 33 (2012), 200-207
80.
Sh. A. Ayupov, K. K. Kudaybergenov, “Additive derivations on algebras of measurable operators”, Journal of Operator Theory, 67 (2012), 495-510
81.
S. Albeverio, Sh. A. Ayupov, K. K. Kudaybergenov, R. Djumamuratov, “Automorphisms of central extensions of type I von Neumann algebras”, Studia Mathematica, 207 (2011), 1-17
82.
S. Albeverio, Sh. A. Ayupov, K. K. Kudaybergenov, B. O. Nurjanov, “Local derivations on algebras of measurable operators”, Communications in Contemporary Mathematics, 13 (2011), 643-657
83.
S. Albeverio, Sh. A. Ayupov, R. Z. Abdullaev, K. K. Kudaybergenov, “Additive derivations on generalized Arens algebras”, Lobachevskii Journal of Mathematics, 32 (2011), 194-202
84.
Sh. A. Ayupov, K. K. Kudaybergenov, T. S. Kalandarov, “The involutive automorphisms of (\tau)-compact operators affiliated with a type I von Neumann algebra”, Methods Funct. Anal. Topology, 14:1 (2008), 54–59
85.
Sh. A. Ayupov, K. K. Kudaybergenov, “Derivations of C*-algebras over the ring of measurable functions”, Uzbek. Mat. Zh., 50:1 (2007), 39–47
86.
Sh. A. Ayupov, K. K. Kudaybergenov, T. S. Kalandarov, “*-automorphisms of the Arens algebra associated with a von Neumann algebra of type I”, Uzbek. Mat. Zh., 50:4 (2007), 9–17
87.
K. K. Kudaǐbergenov, “The Gel'fand-Mazur theorem for $C^*$-algebras over a ring of measurable functions”, Vladikavkaz. Mat. Zh., 8:2 (2006), 45–49
88.
K. K. Kudaybergenov, “A measurable bundle of compact integral operators”, Uzbek. Mat. Zh., 49:1 (2006), 49–57
89.
K. K. Kudaybergenov, “Measurable bundles of operators with a closed range”, Uzbek. Mat. Zh., 48:3 (2005), 54–62
90.
I. G. Ganiev, K. K. Kudaybergenov, “Finite-dimensional modules over a ring of measurable functions”, Uzbek. Mat. Zh., 47:4 (2004), 3–9
91.
K. K. Kudaybergenov, I. G. Ganiev, “Measurable bundles of compact operators”, Methods Funct. Anal. Topology, 7:4 (2001), 1–5
92.
K. K. Kudaybergenov, “Measurable bundles of continuous mappings of cyclic compacta”, Uzbek. Mat. Zh., 43 (2000), 7–14
93.
K. K. Kudaybergenov, “Choquet's theorem for measures with values in the ring of measurable functions”, Uzbek. Mat. Zh., 43:4 (2000), 21–26
94.
K. K. Kudaybergenov, I. G.Ganiev, “Measurable bundles of compact sets”, Uzbek. Mat. Zh., 42:6 (1999), 37–44
95.
Sh. A. Ayupov, V. I. Chilin, R. N. Ganikhodzhaev, K. K. Muminov, A. Artikbaev, B. S. Zakirov, A. Alimov, K. K. Kudaybergenov, F. Mukhamedov, U. Bekboev, I. Rakhimov, “To the memory of Inomjon Gulomjonovich Ganiev”, Vladikavkaz. Mat. Zh., 20:1 (2018), 98–102