01.01.01 (Real analysis, complex analysis, and functional analysis)
Birth date:
7.11.1964
E-mail:
,
Keywords:
W*-algebra; C*-algebra; automorphisms and antiautomorphisms of W*-algebras; real W*-algebra; real C*-algebra; Jordan Banach algebras; JW-algebras; modular theory; traces on komplex and real W*-algebras; weights and states on komplex and real W*-algebras; infinite tensor product; classification of operator algebras; injective factors; injective real factors; hyperfinite factors; hyperfinite real factors; amenable factors; amenable real factors.
Subject:
I am a specialist in the theory operator algebras, in particular, in the theory complex and real von Neumann algebras. My scientific works devoted to the classifications of *-automorphisms and *-antiautomorphisms of complex and real von Neumann algebras, which play an impotant role in the study of the theory of general algebras von Neumann, and to the classification of real factors of type III. Classification of periodic *-antiautomorphisms of hyperfinite factors and classification of periodic *-automorphisms of real hyperfinite factors are obtained. Outer conjugacy classes of automorphisms and antiautomorphisms of real and complex injective factors are descripted. Classification of hyperfinite and injective real factors of type III$_{\lambda}$ ($0)
Main publications:
Jordan, Real and Lie structures in operator algebras. The Monography, Kluwer Academic Publishers, MAIA, 1997, v. 418, 235 p. (with Ayupov Sh. A., Usmanov Sh. .)
Outer conjugacy classes of automorphisms and antiautomorphisms of real and complex injective factors // Journal of Functional Analysis, 1997, vol. 144, 475–485. (with Usmanov Sh. M.)
A. A. Rakhimov, M. E. Nurillaev, Kh. Kh. Boltaev, “Injectivity and nuclearity properties for real C*-algebras”, CMFD, 67:4 (2021), 755–765
2020
2.
A. A. Rakhimov, Kh. Kh. Boltaev, “Index of real subfactors of W*-algebras”, Dal'nevost. Mat. Zh., 20:2 (2020), 234–246
2014
3.
A. A. Rakhimov, “The predual space of a $\mathrm{JBW}^*$-triple”, Eurasian Math. J., 5:3 (2014), 125–128
2012
4.
S. Albeverio, Sh. A. Ayupov, A. A. Rakhimov, R. A. Dadakhodjaev, “Index theory for real factors”, Eurasian Math. J., 3:2 (2012), 12–20
2010
5.
S. Albeverio, Sh. A. Ayupov, R. A. Dadakhodjaev, A. A. Rakhimov, “On Jones' index for real $\mathrm W^*$-algebras”, Eurasian Math. J., 1:4 (2010), 5–19
A. A. Rakhimov, A. A. Katz, R. Dadakhodjaev, “On ideal of compact operators in real factors”, Vladikavkaz. Mat. Zh., 6:1 (2004), 42–45
7.
A. A. Rakhimov, “Action of groups on real factors of type $\mathrm{III}_\lambda$, $\lambda\ne1$”, Zap. Nauchn. Sem. POMI, 315 (2004), 132–148; J. Math. Sci. (N. Y.), 134:4 (2006), 2311–2319
2002
8.
A. A. Rakhimov, A. A. Kats, R. A. Dadakhodjaev, “The Ideal of Compact Operators in Real Factors of Types I and II”, Mat. Tr., 5:1 (2002), 129–134; Siberian Adv. Math., 13:2 (2003), 90–94
Sh. A. Ayupov, A. A. Rakhimov, A. Kh. Abduvaitov, “Real $W^*$-Algebras with Abelian Hermitian Part”, Mat. Zametki, 71:3 (2002), 473–476; Math. Notes, 71:3 (2002), 432–435
A. A. Rakhimov, “Classification for the Actions of a Compact Abelian Group on a Semifinite Real $W^*$-Algebra”, Mat. Tr., 3:2 (2000), 171–181; Siberian Adv. Math., 11:2 (2001), 83–93
A. A. Rakhimov, “On the structure of real injective $W^*$-factors of type III$_{\lambda}$, $0<\lambda<1$”, Zap. Nauchn. Sem. POMI, 255 (1998), 148–163; J. Math. Sci. (New York), 107:4 (2001), 4073–4082
1997
12.
Sh. A. Alimov, A. A. Rakhimov, “On the localization of spectral expansions of distributions in a closed domain”, Differ. Uravn., 33:1 (1997), 80–82; Differ. Equ., 33:1 (1997), 80–82
13.
A. A. Rakhimov, “Injective Real $W^*$-Factors of the Type III$_\lambda$, $0<\lambda<1$”, Funktsional. Anal. i Prilozhen., 31:3 (1997), 88–91; Funct. Anal. Appl., 31:3 (1997), 219–221
A. A. Rakhimov, “Spectral expansions of distributions from negative Sobolev classes”, Differ. Uravn., 32:7 (1996), 1000–1001; Differ. Equ., 32:7 (1996), 1011–1013
15.
Sh. A. Alimov, A. A. Rakhimov, “On the localization of spectral expansions of distributions”, Differ. Uravn., 32:6 (1996), 792–796; Differ. Equ., 32:6 (1996), 798–802
16.
A. A. Rakhimov, “Localization conditions for spectral decompositions related to elliptic operators from the class $A_r$”, Mat. Zametki, 59:3 (1996), 421–427; Math. Notes, 59:3 (1996), 298–302
A. A. Rakhimov, Sh. M. Usmanov, “Periodic ${}^*$-Automorphisms and ${}^*$-Antiautomorphisms of Injective Factors”, Funktsional. Anal. i Prilozhen., 29:1 (1995), 87–89; Funct. Anal. Appl., 29:1 (1995), 68–70
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