KFU. Card publication. Invertibility of the Operators on Hilbert Spaces and Ideals in C*-Algebras

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INVERTIBILITY OF THE OPERATORS ON HILBERT SPACES AND IDEALS IN C*-ALGEBRAS

Form of presentation

Articles in international journals and collections

Year of publication

2022

Язык

английский

Authors, employees of KFU

Bikchentaev Ayrat Midkhatovich, author

Bibliographic description in the original language

Bikchentaev A.M. Invertibility of the Operators on Hilbert Spaces and Ideals in C*-Algebras // Mathematical Notes, 2022, Vol. 112, No. 3, pp. 24–32.

Annotation

Let H be a Hilbert space over the field C, and let B(H) be the ∗-algebra of all linear bounded operators in H. Sufficient conditions for the positivity and invertibility of operators from B(H) are found. An arbitrary symmetry from a von Neumann algebra A is written as the product A^{−1}UA with a positive invertible A and a self-adjoint unitary U from A. Let $\varphi$ be the weight on a von Neumann algebra A, let A ∈ A, and let $\| A \| ≤ 1$. If $A^*A−I ∈ N_{\varphi}$, then $|A|-I\in N_{\varphi}$ and, for any isometry U ∈ A, the inequality $\|A − U\|_{\varphi, 2} ≥ \| |A| − I\|_{\varphi, 2}$ holds. If U is a unitary operator from the polar expansion of the invertible operator A, then this inequality becomes an equality.

Keywords

Hilbert space, linear operator, invertible operator, von Neumann algebra, C-algebra, weight.

The name of the journal

MATHEMATICAL NOTES

Please use this ID to quote from or refer to the card

https://repository.kpfu.ru/eng/?p_id=269301&p_lang=2

Resource files

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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	Bikchentaev A.M. Invertibility of the Operators on Hilbert Spaces and Ideals in C*-Algebras // Mathematical Notes, 2022, Vol. 112, No. 3, pp. 24–32.	ru_RU
dc.identifier.uri	https://repository.kpfu.ru/eng/?p_id=269301&p_lang=2	ru_RU
dc.description.abstract	MATHEMATICAL NOTES	ru_RU
dc.description.abstract	Let H be a Hilbert space over the field C, and let B(H) be the ∗-algebra of all linear bounded operators in H. Sufficient conditions for the positivity and invertibility of operators from B(H) are found. An arbitrary symmetry from a von Neumann algebra A is written as the product A^{−1}UA with a positive invertible A and a self-adjoint unitary U from A. Let $\varphi$ be the weight on a von Neumann algebra A, let A ∈ A, and let $\\| A \\| ≤ 1$. If $A^*A−I ∈ N_{\varphi}$, then $\|A\|-I\in N_{\varphi}$ and, for any isometry U ∈ A, the inequality $\\|A − U\\|_{\varphi, 2} ≥ \\| \|A\| − I\\|_{\varphi, 2}$ holds. If U is a unitary operator from the polar expansion of the invertible operator A, then this inequality becomes an equality.	ru_RU
dc.language.iso	ru	ru_RU
dc.subject	Hilbert space	ru_RU
dc.subject	linear operator	ru_RU
dc.subject	invertible operator	ru_RU
dc.subject	von Neumann algebra	ru_RU
dc.subject	C-algebra	ru_RU
dc.subject	weight.	ru_RU
dc.title	Invertibility of the Operators on Hilbert Spaces and Ideals in C*-Algebras	ru_RU
dc.type	Articles in international journals and collections	ru_RU