dc.contributor.author |
Bikchentaev A. |
|
dc.date.accessioned |
2018-09-18T20:01:06Z |
|
dc.date.available |
2018-09-18T20:01:06Z |
|
dc.date.issued |
2014 |
|
dc.identifier.issn |
0001-4346 |
|
dc.identifier.uri |
https://dspace.kpfu.ru/xmlui/handle/net/135779 |
|
dc.description.abstract |
© 2014, Pleiades Publishing, Ltd. Let τ be a faithful normal semifinite trace on the von Neumann algebra M, 1 ≥ q > 0. The following generalizations of problems 163 and 139 from the book [1] to τ-measurable operators are obtained; it is established that: 1) each τ-compact q-hyponormal operator is normal; 2) if a τ-measurable operator A is normal and, for some natural number n, the operator An is τ-compact, then the operator A is also τ-compact. It is proved that if a τ-measurable operator A is hyponormal and the operator A2 is τ-compact, then the operator A is also τ-compact. A new property of a nonincreasing rearrangement of the product of hyponormal and cohyponormal τ-measurable operators is established. For normal τ-measurable operators A and B, it is shown that the nonincreasing rearrangements of the operators AB and BA coincide. Applications of the results obtained to F-normed symmetric spaces on (M, τ) are considered. |
|
dc.relation.ispartofseries |
Mathematical Notes |
|
dc.subject |
cohyponormal operator |
|
dc.subject |
F-normed symmetric space |
|
dc.subject |
faithful normal semifinite trace |
|
dc.subject |
hyponormal operator |
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dc.subject |
nilpotent |
|
dc.subject |
quasinilpotent |
|
dc.subject |
semifinite von Neumann algebra |
|
dc.subject |
τ-compact operator |
|
dc.subject |
τ-measurable operator |
|
dc.title |
On normal τ-measurable operators affiliated with semifinite von Neumann algebras |
|
dc.type |
Article |
|
dc.relation.ispartofseries-issue |
3-4 |
|
dc.relation.ispartofseries-volume |
96 |
|
dc.collection |
Публикации сотрудников КФУ |
|
dc.relation.startpage |
332 |
|
dc.source.id |
SCOPUS00014346-2014-96-3-4-SID84920917074 |
|