Form of presentation  Articles in international journals and collections 
Year of publication  2022 
Язык  английский 

Bikchentaev Ayrat Midkhatovich, author

Bibliographic description in the original language 
A. M. Bikchentaev, Essentially invertible measurable operators affiliated to a semifinite von Neumann algebra and commutators // Siberian Mathematical Journal, 2022, Vol. 63, No. 2, pp. 224–232. 
Annotation 
Suppose that a von Neumann operator algebra M acts on a Hilbert space H and $\tau$ is a faithful normal semifinite trace on M. If Hermitian operators X, Y lfrom S(M, τ) are such that −X ≤Y ≤ X and Y is $\tau$ essentially invertible then so is X. Let 0 < p ≤ 1. If a phyponormal operator A in S(M, τ) is right $\tau$essentially invertible then A is $\tau$essentially invertible. If a phyponormal operator A in B(H ) is right invertible then A is invertible in B(H ). If a hyponormal operator A in S(M, $\tau$) has a right inverse in S(M, $\tau$) then A is invertible in S(M, $\tau$). If A, T ∈ M and $\mu_t(A^n)^{1/n}
n \to 0$ as $n\to \infty$ for every t > 0 then AT (TA) has no right (left) $\tau$ essential inverse in S(M, $\tau$).
Suppose that H is separable and $\dim H =\infty$. A right (left) essentially invertible operator A in B(H )
is a commutator if and only if the right (left) essential inverse of A is a commutator. 
Keywords 
Hilbert space, linear operator, von Neumann algebra, normal trace, measurable operator, essential invertibility, commutator 
The name of the journal 
SIBERIAN MATHEMATICAL JOURNAL

Please use this ID to quote from or refer to the card 
https://repository.kpfu.ru/eng/?p_id=263668&p_lang=2 
Resource files  

Full metadata record 
Field DC 
Value 
Language 
dc.contributor.author 
Bikchentaev Ayrat Midkhatovich 
ru_RU 
dc.date.accessioned 
20220101T00:00:00Z 
ru_RU 
dc.date.available 
20220101T00:00:00Z 
ru_RU 
dc.date.issued 
2022 
ru_RU 
dc.identifier.citation 
A. M. Bikchentaev, Essentially invertible measurable operators affiliated to a semifinite von Neumann algebra and commutators // Siberian Mathematical Journal, 2022, Vol. 63, No. 2, pp. 224–232. 
ru_RU 
dc.identifier.uri 
https://repository.kpfu.ru/eng/?p_id=263668&p_lang=2 
ru_RU 
dc.description.abstract 
SIBERIAN MATHEMATICAL JOURNAL 
ru_RU 
dc.description.abstract 
Suppose that a von Neumann operator algebra M acts on a Hilbert space H and $\tau$ is a faithful normal semifinite trace on M. If Hermitian operators X, Y lfrom S(M, τ) are such that −X ≤Y ≤ X and Y is $\tau$ essentially invertible then so is X. Let 0 < p ≤ 1. If a phyponormal operator A in S(M, τ) is right $\tau$essentially invertible then A is $\tau$essentially invertible. If a phyponormal operator A in B(H ) is right invertible then A is invertible in B(H ). If a hyponormal operator A in S(M, $\tau$) has a right inverse in S(M, $\tau$) then A is invertible in S(M, $\tau$). If A, T ∈ M and $\mu_t(A^n)^{1/n}
n \to 0$ as $n\to \infty$ for every t > 0 then AT (TA) has no right (left) $\tau$ essential inverse in S(M, $\tau$).
Suppose that H is separable and $\dim H =\infty$. A right (left) essentially invertible operator A in B(H )
is a commutator if and only if the right (left) essential inverse of A is a commutator. 
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 trace 
ru_RU 
dc.subject 
measurable operator 
ru_RU 
dc.subject 
essential invertibility 
ru_RU 
dc.subject 
commutator 
ru_RU 
dc.title 
Essentially invertible measurable operators affiliated to a semifinite von Neumann algebra and commutators 
ru_RU 
dc.type 
Articles in international journals and collections 
ru_RU 
