KFU. Card publication. Hyponormal mesurable operators affiliated to a semifinite von Neumann algebra

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FEDERAL UNIVERSITY

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HYPONORMAL MESURABLE OPERATORS AFFILIATED TO A SEMIFINITE VON NEUMANN ALGEBRA

Form of presentation

Articles in international journals and collections

Year of publication

2025

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Authors, employees of KFU

Bikchentaev Ayrat Midkhatovich, author

Bibliographic description in the original language

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

Annotation

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.

Keywords

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

The name of the journal

SIBERIAN MATHEMATICAL JOURNAL

On-line resource for training course

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

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

https://repository.kpfu.ru/eng/?p_id=314207&p_lang=2

Resource files

File name	Size (MB)	Format
F_simj0656.pdf	0,16	pdf	show / download

Full metadata record

Field DC	Value	Language
dc.contributor.author	Bikchentaev Ayrat Midkhatovich	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/eng/?p_id=314207&p_lang=2	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	Articles in international journals and collections	ru_RU