KFU. Card publication. Commutators and hyponormal operators on a Hilbert space

KAZAN
FEDERAL UNIVERSITY

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COMMUTATORS AND HYPONORMAL OPERATORS ON A HILBERT SPACE

Form of presentation

Articles in international journals and collections

Year of publication

2023

Язык

английский

Authors, employees of KFU

Bikchentaev Ayrat Midkhatovich, author

Ivanshin Petr Nikolaevich, author

Other authors

Akhmadiev Marat Gabdelbyarovich, author

Authors, postgraduates KFU

Alkhasan Khasan , postgraduate kfu

Bibliographic description in the original language

M. Akhmadiev. Commutators and hyponormal operators on a Hilbert space / M. Akhmadiev, H. Alhasan, A. Bikchentaev, P. Ivanshin // J. Iran. Math. Soc. 2023. Vol. 4. № 1. P 67--78.

Annotation

Let H be an innite-dimensional Hilbert space over the field C, B(H) be the ∗-algebra of all linear bounded operators on H. An operator A ∈ B(H) is a commutator, if A = [S, T ] = ST − T S for some S, T ∈ B(H). Let X, Y ∈ B(H) and X ≥ 0. If the operator XY is a non-commutator, then X^pY X^{1−p} is a non-commutator for every 0 < p < 1. Let A ∈ B(H) be p-hyponormal for some 0 < p ≤ 1. If |A^∗|^r is a non-commutator for some r > 0, then |A|^q is a non-commutator for every q > 0. Let H be separable and A ∈ B(H) be a non-commutator. If A is hyponormal (or cohyponormal), then A is normal. We also present results in the case of a finite-dimensional Hilbert space.

Keywords

Hilbert space, linear operator, commutator, hyponormal operator, trace

The name of the journal

Journal of the Iranian Mathematical Society

On-line resource for training course

http://dspace.kpfu.ru/xmlui/bitstream/handle/net/176401/F_JIMS_Volume_4_Issue_1_Pages_67_78.pdf?sequence=1&isAllowed=y

URL

https://dx.doi.org/10.30504/JIMS.2023.393155.1106

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

https://repository.kpfu.ru/eng/?p_id=283141&p_lang=2

Resource files

File name	Size (MB)	Format
F_JIMS_Volume_4_Issue_1_Pages_67_78.pdf	0,37	pdf	show / download

Full metadata record

Field DC	Value	Language
dc.contributor.author	Bikchentaev Ayrat Midkhatovich	ru_RU
dc.contributor.author	Ivanshin Petr Nikolaevich	ru_RU
dc.contributor.author	Akhmadiev Marat Gabdelbyarovich	ru_RU
dc.contributor.author	Alkhasan Khasan	ru_RU
dc.date.accessioned	2023-01-01T00:00:00Z	ru_RU
dc.date.available	2023-01-01T00:00:00Z	ru_RU
dc.date.issued	2023	ru_RU
dc.identifier.citation	M. Akhmadiev. Commutators and hyponormal operators on a Hilbert space / M. Akhmadiev, H. Alhasan, A. Bikchentaev, P. Ivanshin // J. Iran. Math. Soc. 2023. Vol. 4. № 1. P 67--78.	ru_RU
dc.identifier.uri	https://repository.kpfu.ru/eng/?p_id=283141&p_lang=2	ru_RU
dc.description.abstract	Journal of the Iranian Mathematical Society	ru_RU
dc.description.abstract	Let H be an innite-dimensional Hilbert space over the field C, B(H) be the ∗-algebra of all linear bounded operators on H. An operator A ∈ B(H) is a commutator, if A = [S, T ] = ST − T S for some S, T ∈ B(H). Let X, Y ∈ B(H) and X ≥ 0. If the operator XY is a non-commutator, then X^pY X^{1−p} is a non-commutator for every 0 < p < 1. Let A ∈ B(H) be p-hyponormal for some 0 < p ≤ 1. If \|A^∗\|^r is a non-commutator for some r > 0, then \|A\|^q is a non-commutator for every q > 0. Let H be separable and A ∈ B(H) be a non-commutator. If A is hyponormal (or cohyponormal), then A is normal. We also present results in the case of a finite-dimensional Hilbert space.	ru_RU
dc.language.iso	ru	ru_RU
dc.subject	Hilbert space	ru_RU
dc.subject	linear operator	ru_RU
dc.subject	commutator	ru_RU
dc.subject	hyponormal operator	ru_RU
dc.subject	trace	ru_RU
dc.title	Commutators and hyponormal operators on a Hilbert space	ru_RU
dc.type	Articles in international journals and collections	ru_RU