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Mathematics of the USSR-Izvestiya, 1975, Volume 9, Issue 6, Pages 1189–1201
DOI: https://doi.org/10.1070/IM1975v009n06ABEH001517
(Mi im2090)
 

This article is cited in 21 scientific papers (total in 21 papers)

Hereditary and intermediate reflexivity of $W^*$-algebras

A. I. Loginov, V. S. Shulman
References:
Abstract: An operator algebra $R$ is reflexive if every operator which leaves invariant all $R$-invariant subspaces belongs to $R$. The notion of reflexivity can be extended to linear spaces of operators. An operator algebra is said to be hereditarily reflexive if all its weakly closed subspaces are reflexive. This article presents a criterion for the hereditary reflexivity of a $W^*$-algebra, and also examines the more general problem of conditions for the intermediate reflexivity of a pair of $W^*$-algebras. A number of necessary conditions and sufficient conditions for intermediate reflexivity are also obtained.
Bibliography: 20 titles.
Received: 03.04.1974
Bibliographic databases:
UDC: 519.4
MSC: Primary 46L10; Secondary 47A15
Language: English
Original paper language: Russian
Citation: A. I. Loginov, V. S. Shulman, “Hereditary and intermediate reflexivity of $W^*$-algebras”, Math. USSR-Izv., 9:6 (1975), 1189–1201
Citation in format AMSBIB
\Bibitem{LogShu75}
\by A.~I.~Loginov, V.~S.~Shulman
\paper Hereditary and intermediate reflexivity of $W^*$-algebras
\jour Math. USSR-Izv.
\yr 1975
\vol 9
\issue 6
\pages 1189--1201
\mathnet{http://mi.mathnet.ru//eng/im2090}
\crossref{https://doi.org/10.1070/IM1975v009n06ABEH001517}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=405124}
\zmath{https://zbmath.org/?q=an:0327.46073}
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  • https://www.mathnet.ru/eng/im2090
  • https://doi.org/10.1070/IM1975v009n06ABEH001517
  • https://www.mathnet.ru/eng/im/v39/i6/p1260
  • This publication is cited in the following 21 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
    Statistics & downloads:
    Abstract page:346
    Russian version PDF:113
    English version PDF:17
    References:48
    First page:1
     
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