KFU. Card publication. Essentially invertible measurable operators affiliated to a semifinite von Neumann algebra and commutators

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FEDERAL UNIVERSITY

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ESSENTIALLY INVERTIBLE MEASURABLE OPERATORS AFFILIATED TO A SEMIFINITE VON NEUMANN ALGEBRA AND COMMUTATORS

Form of presentation

Articles in international journals and collections

Year of publication

2022

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Authors, employees of KFU

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 p-hyponormal operator A in S(M, τ) is right $\tau$--essentially invertible then A is $\tau$-essentially invertible. If a p-hyponormal 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

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https://repository.kpfu.ru/eng/?p_id=263668&p_lang=2

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Full metadata record

Field DC	Value	Language
dc.contributor.author	Bikchentaev Ayrat Midkhatovich	ru_RU
dc.date.accessioned	2022-01-01T00:00:00Z	ru_RU
dc.date.available	2022-01-01T00:00:00Z	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 p-hyponormal operator A in S(M, τ) is right $\tau$--essentially invertible then A is $\tau$-essentially invertible. If a p-hyponormal 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