1979–1999 — V. I. Romanovskii Institute of Mathematics, Uzbek Acedemy of Sciences, Tashkent, Uzbekistan.
1999–2006 — North Dakota State University, Fargo, ND 58105, USA.
2006–now — Ashford University, Clinton, IA 52732, USA.
Main publications:
Ayupov, Shavkat; Rakhimov, Abdugafur; Usmanov, Shukhrat, Jordan, real and Lie structures in operator algebras, Mathematics and its Applications, 418, Kluwer Publisher Academic Group, Dordrecht, The Netherlands, 1997
Usmanov, Shukhrat, “Operatoroznachnye vesa na veschestvennykh $W^*$-algebrakh i $JW$-algebrakh”, Matematicheskii sbornik, 190:10 (1999), 105–122
Usmanov, Shukhrat, “Teorema dvoistvennosti Takesaki i nepreryvnoe razlozhenie veschestvennykh faktorov tipa III”, Izvestiya RAN, seriya matematicheskaya, 64:4 (2000), 183–200
Sh. M. Usmanov, “Real Factors of Type III$_0$”, Funktsional. Anal. i Prilozhen., 34:1 (2000), 93–95; Funct. Anal. Appl., 34:1 (2000), 76–77
3.
Sh. M. Usmanov, “Takesaki's duality theorem and continuous decomposition for real factors of type III”, Izv. RAN. Ser. Mat., 64:4 (2000), 183–200; Izv. Math., 64:4 (2000), 827–845
Sh. M. Usmanov, “Operator-valued weights on real $W^*$-algebras and reversible $JW$-algebras”, Mat. Sb., 190:10 (1999), 105–122; Sb. Math., 190:10 (1999), 1505–1522
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
Sh. A. Ayupov, Sh. M. Usmanov, “Diameters of state spaces of Jordan Banach algebras”, Izv. Akad. Nauk SSSR Ser. Mat., 53:2 (1989), 227–242; Math. USSR-Izv., 34:2 (1990), 229–244
1985
7.
Sh. M. Usmanov, “Real $W^*$-factors of type III$_\lambda$, $0\le\lambda<1$”, Funktsional. Anal. i Prilozhen., 19:3 (1985), 94–95; Funct. Anal. Appl., 19:3 (1985), 247–249
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