KFU. Card publication. Trace inequalities for Rickart $C^*$-algebras

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TRACE INEQUALITIES FOR RICKART $C^*$-ALGEBRAS

Form of presentation

Articles in international journals and collections

Year of publication

2021

Язык

английский

Authors, employees of KFU

Bikchentaev Ayrat Midkhatovich, author

Bibliographic description in the original language

A. M. Bikchentaev, Trace inequalities for Rickart $C^*$-algebras // Positivity 25 (2021), no. 5, 1943--1957.

Annotation

Rickart $C^*$-algebras are unital and satisfy polar decomposition. We proved that if a unital $C^*$-algebra $\mathcal{A}$ satisfies polar decomposition and admits ``good'' faithful tracial states then $\mathcal{A}$ is a Rickart $C^*$-algebra. Via polar decomposition we characteri\-zed tracial states among all states on a Rickart $C^*$-algebra. We presented the triangle inequality for Hermitian elements and traces on Rickart $C^*$-algebra. For a block projection operator and a trace on a Rickart $C^*$-algebra we proved a new inequality. As a corollary, we obtain a sharp estimate for a trace of the commutator of any Hermitian element and a projection. Also we give a characterization of traces in a wide class of weights on a von Neumann algebra.

Keywords

Hilbert space, polar decomposition, von Neumann algebra, $C^*$-algebra, weight, trace

The name of the journal

POSITIVITY

URL

https://doi.org/10.1007/s11117-021-00852-3

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

https://repository.kpfu.ru/eng/?p_id=255300&p_lang=2

Resource files

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Bikchentaev_2021_Positivity.pdf	0,33	pdf	show / download

Full metadata record

Field DC	Value	Language
dc.contributor.author	Bikchentaev Ayrat Midkhatovich	ru_RU
dc.date.accessioned	2021-01-01T00:00:00Z	ru_RU
dc.date.available	2021-01-01T00:00:00Z	ru_RU
dc.date.issued	2021	ru_RU
dc.identifier.citation	A. M. Bikchentaev, Trace inequalities for Rickart $C^*$-algebras // Positivity 25 (2021), no. 5, 1943--1957.	ru_RU
dc.identifier.uri	https://repository.kpfu.ru/eng/?p_id=255300&p_lang=2	ru_RU
dc.description.abstract	POSITIVITY	ru_RU
dc.description.abstract	Rickart $C^$-algebras are unital and satisfy polar decomposition. We proved that if a unital $C^$-algebra $\mathcal{A}$ satisfies polar decomposition and admits ``good'' faithful tracial states then $\mathcal{A}$ is a Rickart $C^$-algebra. Via polar decomposition we characteri\-zed tracial states among all states on a Rickart $C^$-algebra. We presented the triangle inequality for Hermitian elements and traces on Rickart $C^$-algebra. For a block projection operator and a trace on a Rickart $C^$-algebra we proved a new inequality. As a corollary, we obtain a sharp estimate for a trace of the commutator of any Hermitian element and a projection. Also we give a characterization of traces in a wide class of weights on a von Neumann algebra.	ru_RU
dc.language.iso	ru	ru_RU
dc.subject	Hilbert space	ru_RU
dc.subject	polar decomposition	ru_RU
dc.subject	von Neumann algebra	ru_RU
dc.subject	$C^*$-algebra	ru_RU
dc.subject	weight	ru_RU
dc.subject	trace	ru_RU
dc.title	Trace inequalities for Rickart $C^*$-algebras	ru_RU
dc.type	Articles in international journals and collections	ru_RU