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Izv. Akad. Nauk SSSR Ser. Mat., 1976, Volume 40, Issue 4, Pages 845–854 (Mi izv2206)  

On reductive operators and operator algebras

A. I. Loginov, V. S. Shulman


Abstract: We prove a theorem on the structure of weakly closed reductive operator algebras. The proof essentially relies on a known result of V. I. Lomonosov on transitive operator algebras containing a nonzero compact operator. We deduce a number of corollaries which apply to the reductivity problem.
Bibliography: 20 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1976, 10:4, 799–807

Bibliographic databases:

UDC: 519.4
MSC: Primary 46L15, 47B99; Secondary 46L10
Received: 05.09.1974

Citation: A. I. Loginov, V. S. Shulman, “On reductive operators and operator algebras”, Izv. Akad. Nauk SSSR Ser. Mat., 40:4 (1976), 845–854; Math. USSR-Izv., 10:4 (1976), 799–807

Citation in format AMSBIB
\Bibitem{LogShu76}
\by A.~I.~Loginov, V.~S.~Shulman
\paper On reductive operators and operator algebras
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1976
\vol 40
\issue 4
\pages 845--854
\mathnet{http://mi.mathnet.ru/izv2206}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=428064}
\zmath{https://zbmath.org/?q=an:0332.47009}
\transl
\jour Math. USSR-Izv.
\yr 1976
\vol 10
\issue 4
\pages 799--807
\crossref{https://doi.org/10.1070/IM1976v010n04ABEH001815}


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  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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