KFU. Card publication. Commutators in $C*$-algebras and traces

KAZAN
FEDERAL UNIVERSITY

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COMMUTATORS IN $C*$-ALGEBRAS AND TRACES

Form of presentation

Articles in international journals and collections

Year of publication

2023

Язык

английский

Authors, employees of KFU

Bikchentaev Ayrat Midkhatovich, author

Bibliographic description in the original language

Bikchentaev A. Commutators in $C*$-algebras and traces / Airat Bikchentaev // Annals of Functional Analysis - 2023. Vol. 14. Article number 42. P. 1-14.

Annotation

Let $\mathcal{H}$ be a Hilbert space, $\dim \mathcal{H}= +\infty$. Let $X=U|X|$ be the polar decomposition of an operator $X\in \mathcal{B}(\mathcal{H})$. Then $X$ is a non-commutator if and only if both $U$ and $|X|$ are non-commutators. A Hermitian operator $X\in \mathcal{B}(\mathcal{H})$ is a commutator if and only if the Cayley transform $\mathcal{K}(X)$ is a commutator. Let $\mathcal{H}$ be a Hilbert space and $\dim mathcal{H}\leq +\infty$, $A,B, P\in \mathcal{B}(\mathcal{H})$ and $P=P^2$. If $AB=\lambda BA$ for some $\lambda \in \mathbb{C}\setminus\{1\}$ then the operator $AB$ is a commutator. The operator $AP$ is a commutator if and only if $PA$ is a commutator.

Keywords

Hilbert space, linear operator, commutator, $C^*$-algebra, trace

The name of the journal

Annals of Functional Analysis

On-line resource for training course

http://dspace.kpfu.ru/xmlui/bitstream/handle/net/175256/F_s43034_023_00260_6.pdf?sequence=1&isAllowed=y

URL

https://doi.org/10.1007/s43034-023-00260-6

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

https://repository.kpfu.ru/eng/?p_id=277243&p_lang=2

Resource files

File name	Size (MB)	Format
F_s43034_023_00260_6.pdf	0,41	pdf	show / download

Full metadata record

Field DC	Value	Language
dc.contributor.author	Bikchentaev Ayrat Midkhatovich	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	Bikchentaev A. Commutators in $C*$-algebras and traces / Airat Bikchentaev // Annals of Functional Analysis - 2023. Vol. 14. Article number 42. P. 1-14.	ru_RU
dc.identifier.uri	https://repository.kpfu.ru/eng/?p_id=277243&p_lang=2	ru_RU
dc.description.abstract	Annals of Functional Analysis	ru_RU
dc.description.abstract	Let $\mathcal{H}$ be a Hilbert space, $\dim \mathcal{H}= +\infty$. Let $X=U\|X\|$ be the polar decomposition of an operator $X\in \mathcal{B}(\mathcal{H})$. Then $X$ is a non-commutator if and only if both $U$ and $\|X\|$ are non-commutators. A Hermitian operator $X\in \mathcal{B}(\mathcal{H})$ is a commutator if and only if the Cayley transform $\mathcal{K}(X)$ is a commutator. Let $\mathcal{H}$ be a Hilbert space and $\dim mathcal{H}\leq +\infty$, $A,B, P\in \mathcal{B}(\mathcal{H})$ and $P=P^2$. If $AB=\lambda BA$ for some $\lambda \in \mathbb{C}\setminus\{1\}$ then the operator $AB$ is a commutator. The operator $AP$ is a commutator if and only if $PA$ is a commutator.	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	$C^*$-algebra	ru_RU
dc.subject	trace	ru_RU
dc.title	Commutators in $C*$-algebras and traces	ru_RU
dc.type	Articles in international journals and collections	ru_RU