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Concerning the theory of τ-measurable operators affiliated to a semifinite von Neumann algebra

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dc.contributor.author Bikchentaev A.
dc.date.accessioned 2018-09-18T20:01:06Z
dc.date.available 2018-09-18T20:01:06Z
dc.date.issued 2015
dc.identifier.issn 0001-4346
dc.identifier.uri https://dspace.kpfu.ru/xmlui/handle/net/135780
dc.description.abstract © 2015, Pleiades Publishing, Ltd. Let M be a von Neumann algebra of operators in a Hilbert space H, let τ be an exact normal semifinite trace on M, and let L1(M, τ) be the Banach space of τ-integrable operators. The following results are obtained. If X = X*, Y = Y* are τ-measurable operators and XY ∈ L1(M, τ), then YX ∈ L1(M, τ) and τ(XY) = τ(YX) ∈ R. In particular, if X, Y ∈ B(H)sa and XY ∈ G1, then YX ∈ G1 and tr(XY) = tr(YX) ∈ R. If X ∈ L1(M, τ), then (Formula Presented.). Let A be a τ-measurable operator. If the operator A is τ-compact and V ∈ M is a contraction, then it follows from V* AV = A that V A = AV. We have A = A2 if and only if A = |A*||A|. This representation is also new for bounded idempotents in H. If A = A2 ∈ L1(M, τ), then (Formula Presented.). If A = A2 and A (or A*) is semihyponormal, then A is normal, thus A is a projection. If A = A3 and A is hyponormal or cohyponormal, then A is normal, and thus A = A* ∈ M is the difference of two mutually orthogonal projections (A + A2)/2 and (A2 − A)/2. If A,A2 ∈ L1(M, τ) and A = A3, then τ(A) ∈ R.
dc.relation.ispartofseries Mathematical Notes
dc.subject Banach space of τ-integrable operators
dc.subject cohyponormal operator
dc.subject Hilbert space
dc.subject hyponormal operator
dc.subject idempotent
dc.subject semihyponormal operator
dc.subject von Neumann algebra
dc.subject τ-compact operator
dc.subject τ-measurable operator
dc.title Concerning the theory of τ-measurable operators affiliated to a semifinite von Neumann algebra
dc.type Article
dc.relation.ispartofseries-issue 3-4
dc.relation.ispartofseries-volume 98
dc.collection Публикации сотрудников КФУ
dc.relation.startpage 382
dc.source.id SCOPUS00014346-2015-98-3-4-SID84944882598


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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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