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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 | |
dc.subject | Semifinite trace | |
dc.subject | Von Neumann algebra | |
dc.subject | τ-compact operator | |
dc.subject | τ-essentially invertible operator | |
dc.subject | τ-measurable operator | |
dc.title | On τ-essentially Invertibility of τ-measurable Operators | |
dc.type | Article | |
dc.collection | Публикации сотрудников КФУ | |
dc.source.id | SCOPUS00207748-2019-SID85065677023 |