dc.contributor.author |
Bikchentaev A. |
|
dc.date.accessioned |
2021-02-25T20:42:51Z |
|
dc.date.available |
2021-02-25T20:42:51Z |
|
dc.date.issued |
2020 |
|
dc.identifier.issn |
1385-1292 |
|
dc.identifier.uri |
https://dspace.kpfu.ru/xmlui/handle/net/162276 |
|
dc.description.abstract |
© 2020, Springer Nature Switzerland AG. Let M be a von Neumann algebra of operators on a Hilbert space H and τ be a faithful normal semifinite trace on M. Let tτ be the measure topology on the ∗ -algebra S(M, τ) of all τ-measurable operators. We define three tτ-closed classes P1, P2 and P3 of τ-measurable operators and investigate their properties. The class P2 contains P1∪ P3. If a τ-measurable operator T is hyponormal, then T lies in P1∩ P3; if an operator T lies in P3, then UTU∗ belongs to P3 for all isometries U from M. If a bounded operator T lies in P1∪ P3 then T is normaloid. If an operator T∈ S(M, τ) is p-hyponormal with 0 < p≤ 1 then T∈ P1. If M= B(H) and τ=tr is the canonical trace, then the class P1 (resp., P3) coincides with the set of all paranormal (resp., ∗ -paranormal) operators on H. Let A, B∈ S(M, τ) and A be p-hyponormal with 0 < p≤ 1. If AB is τ-compact then A∗B is τ-compact. |
|
dc.relation.ispartofseries |
Positivity |
|
dc.subject |
Generalized singular value function |
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dc.subject |
Hilbert space |
|
dc.subject |
Hyponormal operator |
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dc.subject |
Measurable operator |
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dc.subject |
Non-commutative integration |
|
dc.subject |
Operator inequality |
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dc.subject |
Paranormal operator |
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dc.subject |
Trace |
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dc.subject |
von Neumann algebra |
|
dc.title |
Paranormal measurable operators affiliated with a semifinite von Neumann algebra. II |
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dc.type |
Article |
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dc.relation.ispartofseries-issue |
5 |
|
dc.relation.ispartofseries-volume |
24 |
|
dc.collection |
Публикации сотрудников КФУ |
|
dc.relation.startpage |
1487 |
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dc.source.id |
SCOPUS13851292-2020-24-5-SID85081021568 |
|