Form of presentation  Articles in international journals and collections 
Year of publication  2021 
Язык  английский 

Bikchentaev Ayrat Midkhatovich, author

Bibliographic description in the original language 
A. M. Bikchentaev, Trace inequalities for Rickart $C^*$algebras // Positivity 25 (2021), no. 5, 19431957. 
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/s11117021008523 
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  

Full metadata record 
Field DC 
Value 
Language 
dc.contributor.author 
Bikchentaev Ayrat Midkhatovich 
ru_RU 
dc.date.accessioned 
20210101T00:00:00Z 
ru_RU 
dc.date.available 
20210101T00:00:00Z 
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, 19431957. 
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 
