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# On idempotent τ-measurable operators affiliated to a von Neumann algebra

 dc.contributor.author Bikchentaev A. dc.date.accessioned 2018-09-19T20:02:53Z dc.date.available 2018-09-19T20:02:53Z dc.date.issued 2016 dc.identifier.issn 0001-4346 dc.identifier.uri https://dspace.kpfu.ru/xmlui/handle/net/142489 dc.description.abstract © 2016, Pleiades Publishing, Ltd.Let τ be a faithful normal semifinite trace on a von Neumann algebra M, let p, 0 < p < ∞, be a number, and let Lp(M, τ) be the space of operators whose pth power is integrable (with respect to τ). Let P and Q be τ-measurable idempotents, and let A ≡ P − Q. In this case, 1) if A ≥ 0, then A is a projection and QA = AQ = 0; 2) if P is quasinormal, then P is a projection; 3) if Q ∈ M and A ∈ Lp(M, τ), then A2 ∈ Lp(M, τ). Let n be a positive integer, n > 2, and A = An ∈ M. In this case, 1) if A ≠ 0, then the values of the nonincreasing rearrangement μt(A) belong to the set {0} ∪ [‖An−2‖−1, ‖A‖] for all t > 0; 2) either μt(A) ≥ 1 for all t > 0 or there is a t0 > 0 such that μt(A) = 0 for all t > t0. For every τ-measurable idempotent Q, there is aunique rank projection P ∈ M with QP = P, PQ = Q, and PM = QM. There is a unique decomposition Q = P + Z, where Z2 = 0, ZP = 0, and PZ = Z. Here, if Q ∈ Lp(M, τ), then P is integrable, and τ(Q) = τ(P) for p = 1. If A ∈ L1(M, τ) and if A = A3 and A − A2 ∈ M, then τ(A) ∈ R. dc.relation.ispartofseries Mathematical Notes dc.subject Hilbert space dc.subject idempotent dc.subject integrable operator dc.subject non-increasing rearrangement dc.subject normal trace dc.subject projection dc.subject quasinormal operator dc.subject rank projection dc.subject von Neumann algebra dc.subject τ-compact operator dc.subject τ-measurable operator dc.title On idempotent τ-measurable operators affiliated to a von Neumann algebra dc.type Article dc.relation.ispartofseries-issue 3-4 dc.relation.ispartofseries-volume 100 dc.collection Публикации сотрудников КФУ dc.relation.startpage 515 dc.source.id SCOPUS00014346-2016-100-34-SID84992111228
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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.