dc.contributor.author |
Bikchentaev A. |
|
dc.date.accessioned |
2020-01-21T20:31:09Z |
|
dc.date.available |
2020-01-21T20:31:09Z |
|
dc.date.issued |
2019 |
|
dc.identifier.issn |
0020-7748 |
|
dc.identifier.uri |
https://dspace.kpfu.ru/xmlui/handle/net/157318 |
|
dc.description.abstract |
© 2019, Springer Science+Business Media, LLC, part of Springer Nature. Let ℳ be a von Neumann algebra of operators on a Hilbert space and τ be a faithful normal semifinite trace on ℳ. Let I be the unit of the algebra ℳ. A τ-measurable operator A is said to be τ-essentially right (or left) invertible if there exists a τ-measurable operator B such that the operator I − AB (or I − BA) is τ-compact. A necessary and sufficient condition for an operator A to be τ-essentially left invertible is that A ∗ A (or, equivalently, A∗A) is τ-essentially invertible. We present a sufficient condition that a τ-measurable operator A not be τ-essentially left invertible. For τ-measurable operators A and P = P 2 the following conditions are equivalent: 1. A is τ-essential right inverse for P; 2. A is τ-essential left inverse for P; 3. I − A,I − P are τ-compact; 4. PA is τ-essential left inverse for P. For τ-measurable operators A = A 3 , B = B 3 the following conditions are equivalent: 1. B is τ-essential right inverse for A; 2. B is τ-essential left inverse for A. Pairs of faithful normal semifinite traces on ℳ are considered. |
|
dc.relation.ispartofseries |
International Journal of Theoretical Physics |
|
dc.subject |
Hilbert space |
|
dc.subject |
Idempotent |
|
dc.subject |
Measure topology |
|
dc.subject |
Normal weight |
|
dc.subject |
Rearrangement |
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dc.subject |
Semifinite trace |
|
dc.subject |
Von Neumann algebra |
|
dc.subject |
τ-compact operator |
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dc.subject |
τ-essentially invertible operator |
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dc.subject |
τ-measurable operator |
|
dc.title |
On τ-essentially Invertibility of τ-measurable Operators |
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dc.type |
Article |
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dc.collection |
Публикации сотрудников КФУ |
|
dc.source.id |
SCOPUS00207748-2019-SID85065677023 |
|