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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
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
Citation:
A. I. Loginov, V. S. Shulman, “Hereditary and intermediate reflexivity of $W^*$-algebras”, Math. USSR-Izv., 9:6 (1975), 1189–1201
Linking options:
https://www.mathnet.ru/eng/im2090https://doi.org/10.1070/IM1975v009n06ABEH001517 https://www.mathnet.ru/eng/im/v39/i6/p1260
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Abstract page: | 346 | Russian version PDF: | 113 | English version PDF: | 17 | References: | 48 | First page: | 1 |
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