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, affiliated with a seminite von Neumann algebra //
Russian Mathematics, 2020, Vol. 64, No. 5, pp. 7982.

Annotation 
Let $\tau$ be a faithful normal seminite trace on a von Neumann algebra. We establish the Leibniz criterion for signalternating series of $\tau$measurable operators and present an analogue of the criterion of series «sandwich« series for $\tau$measurable operators. We prove a
refinement 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 
20200101T00:00:00Z 
ru_RU 
dc.date.available 
20200101T00:00:00Z 
ru_RU 
dc.date.issued 
2020 
ru_RU 
dc.identifier.citation 
A.M. Bikchentaev, Convergence in measure and $\tau$compactness of $\tau$measurable
operators, affiliated with a seminite von Neumann algebra //
Russian Mathematics, 2020, Vol. 64, No. 5, pp. 7982.

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 seminite trace on a von Neumann algebra. We establish the Leibniz criterion for signalternating series of $\tau$measurable operators and present an analogue of the criterion of series «sandwich« series for $\tau$measurable operators. We prove a
refinement 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, affiliated with a seminite von Neumann algebra 
ru_RU 
dc.type 
Articles in international journals and collections 
ru_RU 
