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On the $\tau$-compactness of products of $\tau$-measurable operators adjoint to semi-finite von Neumann algebras

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dc.contributor Казанский федеральный университет
dc.contributor.author Bikchentaev Airat Midkhatovich
dc.date.accessioned 2019-08-05T11:27:42Z
dc.date.available 2019-08-05T11:27:42Z
dc.date.issued 2019
dc.identifier.citation Bikchentaev A.M. On the $\tau$-compactness of products of $\tau$-measurable operators adjoint to semi-finite von Neumann algebras / A.M. Bikchentaev // Journal of Mathematical Sciences. - 2019. - 241 (4). - P. 458-468.
dc.identifier.uri https://dspace.kpfu.ru/xmlui/handle/net/151521
dc.description.abstract Let M be the von Neumann algebra of operators in a Hilbert space H and $\tau$ be an exact normal semi-finite trace on M. We obtain inequalities for permutations of products of $\tau$-measurable operators. We apply these inequalities to obtain new submajorizations (in the sense of Hardy, Littlewood, and P´olya) of products of $\tau$-measurable operators and a sufficient condition of orthogonality of certain nonnegative $\tau$-measurable operators. We state sufficient conditions of the $\tau$-compactness of products of self-adjoint $\tau$-measurable operators and obtain a criterion of the $\tau$-compactness of the product of a nonnegative $\tau$-measurable operator and an arbitrary $\tau$-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 $\tau$ = tr.
dc.language.iso en
dc.relation.ispartofseries Journal of Mathematical Sciences (United States)
dc.rights открытый доступ
dc.subject Hilbert space
dc.subject linear operator
dc.subject von Neumann algebra
dc.subject normal semi-finite trace
dc.subject $\tau$-measurable operator
dc.subject $\tau$-compact operator
dc.subject elementary operator
dc.subject nilpotent
dc.subject permutation
dc.subject submajorization.
dc.subject.other Математика
dc.title On the $\tau$-compactness of products of $\tau$-measurable operators adjoint to semi-finite von Neumann algebras
dc.type Article
dc.contributor.org Институт математики и механики им.Н.И.Лобачевского
dc.description.pages 458-468
dc.relation.ispartofseries-issue 4
dc.relation.ispartofseries-volume 241
dc.pub-id 205879
dc.identifier.doi 10.1007/s10958-019-04437-0


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