КФУ. Карточка публикации. Hyponormal mesurable operators affiliated to a semifinite von Neumann algebra

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HYPONORMAL MESURABLE OPERATORS AFFILIATED TO A SEMIFINITE VON NEUMANN ALGEBRA

Форма представления

Статьи в зарубежных журналах и сборниках

Год публикации

2025

Язык

английский

Авторы, сотрудники КФУ

Бикчентаев Айрат Мидхатович, автор

Библиографическое описание на языке оригинала

A. M. Bikchentaev, Hyponormal mesurable operators affiliated to a semifinite von Neumann algebra // Siberian Mathematical Journal. — 2025. — Vol. 66. — No. 3. — pp. 656–663.

Аннотация

Let τ be a faithful normal semifinite trace on a von Neumann algebra M. We study the cases when a hyponormal τ-measurable operator (or a estriction of it) is normal. We obtain a criterion for the hyponormality of a -measurable operator in terms of its singular value function. The set of all τ-measurable hyponormal operators is closed in the topology of τ -local convergence in measure. This assertion is a generalization of Problem 226 from the book “Halmos P.R., A Hilbert Space Problem Book, Second edition, Springer, New York (1982)” to the setting of unbounded operators. The set of all τ-measurable cohyponormal operators is closed in the topology of τ -local convergence in measure if and only if the von Neumann algebra M is finite.

Ключевые слова

Hilbert space, von Neumann algebra, normal trace, measurable operator, hyponormal operator 1

Название журнала

SIBERIAN MATHEMATICAL JOURNAL

Ссылка для РПД

http://dspace.kpfu.ru/xmlui/bitstream/handle/net/185259/F_simj0656.pdf?sequence=1&isAllowed=y

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https://repository.kpfu.ru/?p_id=314207

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Полная запись метаданных

Поле DC	Значение	Язык
dc.contributor.author	Бикчентаев Айрат Мидхатович	ru_RU
dc.date.accessioned	2025-01-01T00:00:00Z	ru_RU
dc.date.available	2025-01-01T00:00:00Z	ru_RU
dc.date.issued	2025	ru_RU
dc.identifier.citation	A. M. Bikchentaev, Hyponormal mesurable operators affiliated to a semifinite von Neumann algebra // Siberian Mathematical Journal. — 2025. — Vol. 66. — No. 3. — pp. 656–663.	ru_RU
dc.identifier.uri	https://repository.kpfu.ru/?p_id=314207	ru_RU
dc.description.abstract	SIBERIAN MATHEMATICAL JOURNAL	ru_RU
dc.description.abstract	Let τ be a faithful normal semifinite trace on a von Neumann algebra M. We study the cases when a hyponormal τ-measurable operator (or a estriction of it) is normal. We obtain a criterion for the hyponormality of a -measurable operator in terms of its singular value function. The set of all τ-measurable hyponormal operators is closed in the topology of τ -local convergence in measure. This assertion is a generalization of Problem 226 from the book “Halmos P.R., A Hilbert Space Problem Book, Second edition, Springer, New York (1982)” to the setting of unbounded operators. The set of all τ-measurable cohyponormal operators is closed in the topology of τ -local convergence in measure if and only if the von Neumann algebra M is finite.	ru_RU
dc.language.iso	ru	ru_RU
dc.subject	Hilbert space	ru_RU
dc.subject	von Neumann algebra	ru_RU
dc.subject	normal trace	ru_RU
dc.subject	measurable operator	ru_RU
dc.subject	hyponormal operator 1	ru_RU
dc.title	Hyponormal mesurable operators affiliated to a semifinite von Neumann algebra	ru_RU
dc.type	Статьи в зарубежных журналах и сборниках	ru_RU