KFU. Card publication. Hyponormal measurable operators affiliated with a semifinite von Neumann algebra. IV

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HYPONORMAL MEASURABLE OPERATORS AFFILIATED WITH A SEMIFINITE VON NEUMANN ALGEBRA. IV

Form of presentation

Articles in international journals and collections

Year of publication

2026

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Authors, employees of KFU

Bikchentaev Ayrat Midkhatovich, author

Bibliographic description in the original language

Bikchentaev A. M., Hyponormal measurable operators affiliated with a semifinite von Neumann algebra. IV // Siberian Mathematical Journal. — 2026. — Vol. 67. — � 1. — Pp. 10--17.

Annotation

Let τ be a faithful normal semifinite trace on a von Neumann algebra M of operators. For a normal operator A in M, a condition on a τ-integrable operator B is found under which the operator A + B is normal. For an operator whose square is τ -integrable, equivalent conditions for its normality are established in terms of trace inequalities. For an operator in M, a criterion for hyponormality is found in terms of trace inequalities. It is shown that, given an arbitrary natural n, the power (PQ)n of the product of projections P and Q in M is hyponormal if and only if PQ = QP. Operator inequalities are obtained for powers of hyponormal contractions. It is shown that every natural power of a hyponormal partial isometry is a hyponormal partial isometry with the same initial space.

Keywords

Hilbert space, von Neumann algebra, normal trace, measurable operator, hyponormal operator, partial isometry

The name of the journal

SIBERIAN MATHEMATICAL JOURNAL

On-line resource for training course

http://dspace.kpfu.ru/xmlui/bitstream/handle/net/185669/F_simj0010.pdf?sequence=1&isAllowed=y

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

https://repository.kpfu.ru/eng/?p_id=323402&p_lang=2

Resource files

File name	Size (MB)	Format
F_simj0010.pdf	0,16	pdf	show / download

Full metadata record

Field DC	Value	Language
dc.contributor.author	Bikchentaev Ayrat Midkhatovich	ru_RU
dc.date.accessioned	2026-01-01T00:00:00Z	ru_RU
dc.date.available	2026-01-01T00:00:00Z	ru_RU
dc.date.issued	2026	ru_RU
dc.identifier.citation	Bikchentaev A. M., Hyponormal measurable operators affiliated with a semifinite von Neumann algebra. IV // Siberian Mathematical Journal. — 2026. — Vol. 67. — � 1. — Pp. 10--17.	ru_RU
dc.identifier.uri	https://repository.kpfu.ru/eng/?p_id=323402&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 of operators. For a normal operator A in M, a condition on a τ-integrable operator B is found under which the operator A + B is normal. For an operator whose square is τ -integrable, equivalent conditions for its normality are established in terms of trace inequalities. For an operator in M, a criterion for hyponormality is found in terms of trace inequalities. It is shown that, given an arbitrary natural n, the power (PQ)n of the product of projections P and Q in M is hyponormal if and only if PQ = QP. Operator inequalities are obtained for powers of hyponormal contractions. It is shown that every natural power of a hyponormal partial isometry is a hyponormal partial isometry with the same initial space.	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	ru_RU
dc.subject	partial isometry	ru_RU
dc.title	Hyponormal measurable operators affiliated with a semifinite von Neumann algebra. IV	ru_RU
dc.type	Articles in international journals and collections	ru_RU