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On the τ-Compactness of Products of τ -Measurable Operators Adjoint to Semi-Finite Von Neumann Algebras

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dc.contributor.author Bikchentaev A.
dc.date.accessioned 2020-01-15T21:46:07Z
dc.date.available 2020-01-15T21:46:07Z
dc.date.issued 2019
dc.identifier.issn 1072-3374
dc.identifier.uri https://dspace.kpfu.ru/xmlui/handle/net/155768
dc.description.abstract © 2019, Springer Science+Business Media, LLC, part of Springer Nature. Let M be the von Neumann algebra of operators in a Hilbert space H and τ be an exact normal semi-finite trace on M. We obtain inequalities for permutations of products of τ-measurable operators. We apply these inequalities to obtain new submajorizations (in the sense of Hardy, Littlewood, and Pólya) of products of τ -measurable operators and a sufficient condition of orthogonality of certain nonnegative τ-measurable operators. We state sufficient conditions of the τ –compactness of products of self-adjoint τ -measurable operators and obtain a criterion of the τ -compactness of the product of a nonnegative τ-measurable operator and an arbitrary τ -measurable operator. We present an example that shows that the nonnegativity of one of the factors is substantial. We also state a criterion of the elementary nature of the product of nonnegative operators from M. All results are new for the *-algebra B(H) of all bounded linear operators in H endowed with the canonical trace τ = tr.
dc.relation.ispartofseries Journal of Mathematical Sciences (United States)
dc.subject 46L51
dc.subject 47C15
dc.subject elementary operator
dc.subject Hilbert space
dc.subject linear operator
dc.subject nilpotent
dc.subject normal semi-finite trace
dc.subject permutation
dc.subject submajorization
dc.subject von Neumann algebra
dc.subject τ -compact operator
dc.subject τ -measurable operator
dc.title On the τ-Compactness of Products of τ -Measurable Operators Adjoint to Semi-Finite Von Neumann Algebras
dc.type Article
dc.relation.ispartofseries-issue 4
dc.relation.ispartofseries-volume 241
dc.collection Публикации сотрудников КФУ
dc.relation.startpage 458
dc.source.id SCOPUS10723374-2019-241-4-SID85069918952


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  • Публикации сотрудников КФУ Scopus [24551]
    Коллекция содержит публикации сотрудников Казанского федерального (до 2010 года Казанского государственного) университета, проиндексированные в БД Scopus, начиная с 1970г.

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