Form of presentation  Articles in international journals and collections 
Year of publication  2019 
Язык  английский 

Bikchentaev Ayrat Midkhatovich, author

Bibliographic description in the original language 
Bikchentaev A.M. On the $\tau$compactness of products of $\tau$measurable operators adjoint to semifinite von Neumann algebras / A.M. Bikchentaev // Journal of Mathematical Sciences.  2019.  241 (4).  P. 458468. 
Annotation 
Let M be the von Neumann algebra of operators in a Hilbert space H and $\tau$ be an exact
normal semifinite trace on M. We obtain inequalities for permutations of products of $\tau$measurable
operators. We apply these inequalities to obtain new submajorizations (in the sense of Hardy, Littlewood,
and P´olya) of products of $\tau$measurable operators and a sufficient condition of orthogonality
of certain nonnegative $\tau$measurable operators. We state sufficient conditions of the $\tau$compactness
of products of selfadjoint $\tau$measurable operators and obtain a criterion of the $\tau$compactness of the
product of a nonnegative $\tau$measurable operator and an arbitrary $\tau$measurable operator. We present
an example that shows that the nonnegativity of one of the factors is substantial. We also state a
criterion of the elementary nature of the product of nonnegative operators from M. All results are
new for the *algebra B(H) of all bounded linear operators in H endowed with the canonical trace
$\tau$ = tr. 
Keywords 
Hilbert space, linear operator, von Neumann algebra, normal semifinite
trace, $\tau$measurable operator, $\tau$compact operator, elementary operator, nilpotent, permutation, submajorization. 
The name of the journal 
Journal of Mathematical Sciences (United States)

Online resource for training course 
http://dspace.kpfu.ru/xmlui/bitstream/handle/net/151521/Bikchentaev_2019_Journal_of_Mathematical_Sciences.pdf?sequence=1&isAllowed=y

Please use this ID to quote from or refer to the card 
https://repository.kpfu.ru/eng/?p_id=205879&p_lang=2 
Resource files  

Full metadata record 
Field DC 
Value 
Language 
dc.contributor.author 
Bikchentaev Ayrat Midkhatovich 
ru_RU 
dc.date.accessioned 
20190101T00:00:00Z 
ru_RU 
dc.date.available 
20190101T00:00:00Z 
ru_RU 
dc.date.issued 
2019 
ru_RU 
dc.identifier.citation 
Bikchentaev A.M. On the $\tau$compactness of products of $\tau$measurable operators adjoint to semifinite von Neumann algebras / A.M. Bikchentaev // Journal of Mathematical Sciences.  2019.  241 (4).  P. 458468. 
ru_RU 
dc.identifier.uri 
https://repository.kpfu.ru/eng/?p_id=205879&p_lang=2 
ru_RU 
dc.description.abstract 
Journal of Mathematical Sciences (United States) 
ru_RU 
dc.description.abstract 
Let M be the von Neumann algebra of operators in a Hilbert space H and $\tau$ be an exact
normal semifinite trace on M. We obtain inequalities for permutations of products of $\tau$measurable
operators. We apply these inequalities to obtain new submajorizations (in the sense of Hardy, Littlewood,
and P´olya) of products of $\tau$measurable operators and a sufficient condition of orthogonality
of certain nonnegative $\tau$measurable operators. We state sufficient conditions of the $\tau$compactness
of products of selfadjoint $\tau$measurable operators and obtain a criterion of the $\tau$compactness of the
product of a nonnegative $\tau$measurable operator and an arbitrary $\tau$measurable operator. We present
an example that shows that the nonnegativity of one of the factors is substantial. We also state a
criterion of the elementary nature of the product of nonnegative operators from M. All results are
new for the *algebra B(H) of all bounded linear operators in H endowed with the canonical trace
$\tau$ = tr. 
ru_RU 
dc.language.iso 
ru 
ru_RU 
dc.subject 
Hilbert space 
ru_RU 
dc.subject 
linear operator 
ru_RU 
dc.subject 
von Neumann algebra 
ru_RU 
dc.subject 
normal semifinite
trace 
ru_RU 
dc.subject 
$\tau$measurable operator 
ru_RU 
dc.subject 
$\tau$compact operator 
ru_RU 
dc.subject 
elementary operator 
ru_RU 
dc.subject 
nilpotent 
ru_RU 
dc.subject 
permutation 
ru_RU 
dc.subject 
submajorization. 
ru_RU 
dc.title 
On the $\tau$compactness of products of $\tau$measurable operators adjoint to semifinite von Neumann algebras 
ru_RU 
dc.type 
Articles in international journals and collections 
ru_RU 
