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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 |