| Form of presentation | Articles in international journals and collections |
| Year of publication | 2020 |
| Язык | английский |
|
Bikchentaev Ayrat Midkhatovich, author
|
| Bibliographic description in the original language |
A.M. Bikchentaev, Convergence in measure and $\tau$-compactness of $\tau$ -measurable
operators, affi liated with a semi nite von Neumann algebra //
Russian Mathematics, 2020, Vol. 64, No. 5, pp. 79-82.
|
| Annotation |
Let $\tau$ be a faithful normal semi nite trace on a von Neumann algebra. We establish the Leibniz criterion for sign-alternating series of $\tau$ -measurable operators and present an analogue of the criterion of series «sandwich« series for $\tau$ -measurable operators. We prove a
refi nement of this criterion for the $\tau$-compact case. In terms of measure convergence topology, the criterion of $\tau$ -compactness of an arbitrary $\tau$-measurable operator is established. We also give a suffient condition of 1) $\tau$ -compactness of the commutator of a \tau$ -measurable operator and a projection; 2) convergence of $\tau$-measurable operator and projection
commutator sequences to the zero operator in the measure $\tau$ .
|
| Keywords |
Hilbert space, von Neumann algebra, normal trace, measurable operator, topology of convergence in measure, series of operators, $\tau$ -compact operator. |
| The name of the journal |
Russian Mathematics
|
| Please use this ID to quote from or refer to the card |
https://repository.kpfu.ru/eng/?p_id=232626&p_lang=2 |
| Resource files | |
|
|
Full metadata record  |
| Field DC |
Value |
Language |
| dc.contributor.author |
Bikchentaev Ayrat Midkhatovich |
ru_RU |
| dc.date.accessioned |
2020-01-01T00:00:00Z |
ru_RU |
| dc.date.available |
2020-01-01T00:00:00Z |
ru_RU |
| dc.date.issued |
2020 |
ru_RU |
| dc.identifier.citation |
A.M. Bikchentaev, Convergence in measure and $\tau$-compactness of $\tau$ -measurable
operators, affi liated with a semi nite von Neumann algebra //
Russian Mathematics, 2020, Vol. 64, No. 5, pp. 79-82.
|
ru_RU |
| dc.identifier.uri |
https://repository.kpfu.ru/eng/?p_id=232626&p_lang=2 |
ru_RU |
| dc.description.abstract |
Russian Mathematics |
ru_RU |
| dc.description.abstract |
Let $\tau$ be a faithful normal semi nite trace on a von Neumann algebra. We establish the Leibniz criterion for sign-alternating series of $\tau$ -measurable operators and present an analogue of the criterion of series «sandwich« series for $\tau$ -measurable operators. We prove a
refi nement of this criterion for the $\tau$-compact case. In terms of measure convergence topology, the criterion of $\tau$ -compactness of an arbitrary $\tau$-measurable operator is established. We also give a suffient condition of 1) $\tau$ -compactness of the commutator of a \tau$ -measurable operator and a projection; 2) convergence of $\tau$-measurable operator and projection
commutator sequences to the zero operator in the measure $\tau$ .
|
ru_RU |
| dc.language.iso |
ru |
ru_RU |
| dc.subject |
Hilbert space |
ru_RU |
| dc.subject |
von Neumann algebra |
ru_RU |
| dc.subject |
normal trace |
ru_RU |
| dc.subject |
measurable operator |
ru_RU |
| dc.subject |
topology of convergence in measure |
ru_RU |
| dc.subject |
series of operators |
ru_RU |
| dc.subject |
$\tau$ -compact operator. |
ru_RU |
| dc.title |
Convergence in measure and $\tau$-compactness of $\tau$ -measurable operators, affi liated with a semi nite von Neumann algebra |
ru_RU |
| dc.type |
Articles in international journals and collections |
ru_RU |
|
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