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dc.contributor.author | Bikchentaev A. | |
dc.date.accessioned | 2019-01-22T20:51:41Z | |
dc.date.available | 2019-01-22T20:51:41Z | |
dc.date.issued | 2018 | |
dc.identifier.issn | 1995-0802 | |
dc.identifier.uri | https://dspace.kpfu.ru/xmlui/handle/net/149140 | |
dc.description.abstract | © 2018, Pleiades Publishing, Ltd. Let M be a von Neumann algebra of operators on a Hilbert space H, τ be a faithful normal semifinite trace on M. We define two (closed in the topology of convergence in measure τ) classes P1and P2of τ-measurable operators and investigate their properties. The class P2contains P1. If a τ-measurable operator T is hyponormal, then T lies in P1; if an operator T lies in Pk, then UTU* belongs to Pkfor all isometries U from Mand k = 1, 2; if an operator T from P1admits the bounded inverse T−1then T−1lies in P1. If a bounded operator T lies in P1then T is normaloid, Tnbelongs to P1and a rearrangement μt(Tn) ≥ μt(T)nfor all t > 0 and natural n. If a τ-measurable operator T is hyponormal and Tnis τ-compact operator for some natural number n then T is both normal and τ-compact. If an operator T lies in P1then T 2 belongs to P1. If M= B(H) and τ = tr, then the class P1coincides with the set of all paranormal operators onH. If a τ-measurable operator A is q-hyponormal (1 ≥ q > 0) and |A*| ≥ μ∞(A)I then Ais normal. In particular, every τ-compact q-hyponormal (or q-cohyponormal) operator is normal. Consider a τ-measurable nilpotent operator Z ≠ 0 and numbers a, b ∈ R. Then an operator Z*Z − ZZ* + aRZ + bSZ cannot be nonpositive or nonnegative. Hence a τ-measurable hyponormal operator Z ≠ 0 cannot be nilpotent. | |
dc.relation.ispartofseries | Lobachevskii Journal of Mathematics | |
dc.subject | Hilbert space | |
dc.subject | hyponormal operator | |
dc.subject | integrable operator | |
dc.subject | measure topology | |
dc.subject | nilpotent | |
dc.subject | normal semifinite trace | |
dc.subject | paranormal operator | |
dc.subject | projection | |
dc.subject | rearrangement | |
dc.subject | von Neumann algebra | |
dc.subject | τ-compact operator | |
dc.subject | τ-measurable operator | |
dc.title | Paranormal Measurable Operators Affiliated with a Semifinite von Neumann Algebra | |
dc.type | Article | |
dc.relation.ispartofseries-issue | 6 | |
dc.relation.ispartofseries-volume | 39 | |
dc.collection | Публикации сотрудников КФУ | |
dc.relation.startpage | 731 | |
dc.source.id | SCOPUS19950802-2018-39-6-SID85051067313 |