КФУ. Карточка публикации. 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

Форма представления

Статьи в зарубежных журналах и сборниках

Год публикации

2022

Язык

английский

Авторы, сотрудники КФУ

Бикчентаев Айрат Мидхатович, автор

Библиографическое описание на языке оригинала

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.

Аннотация

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.

Ключевые слова

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

Название журнала

MATHEMATICAL NOTES

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Полная запись метаданных

Поле DC	Значение	Язык
dc.contributor.author	Бикчентаев Айрат Мидхатович	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/?p_id=269301	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	Статьи в зарубежных журналах и сборниках	ru_RU