KFU. Card publication. Ultraproducts for State-Spaces of C∗-Algebra and Radon Measures

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FEDERAL UNIVERSITY

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ULTRAPRODUCTS FOR STATE-SPACES OF C∗-ALGEBRA AND RADON MEASURES

Form of presentation

Articles in international journals and collections

Year of publication

2020

Язык

русский

Authors, employees of KFU

Khaliullin Samigulla Garifullovich, author

Bibliographic description in the original language

Haliullin, S.G. Ultraproducts for State-Spaces of C∗-Algebra and Radon Measures / Haliullin, S.G // Lobachevskii Journal of Mathematics. -2020. - 41(4). - P. 655–660

Annotation

This paper deals with properties of the ultraproducts for various structures. We introduce and study the concept of the ergodic action of a group with respect to a normal state on an abelian von Neumann algebra. In particular, we provide an example showing that the ultraproduct of ergodic states, generally speaking, is not ergodic. The ultraproduct of the Radon measures on a compact convex subset of a locally convex space is also investigated in the paper. As is well-known, the study of the extreme points in the state set for a C∗−algebra is a very interesting problem in itself. Considering the ultraproducts of C∗-algebras and the states on these algebras, we get quite nontrivial results.

Keywords

ultraproduct, state-space, Radon measure

The name of the journal

Lobachevskii Journal of Mathematics (international electronic journal)

URL

https://link.springer.com/article/10.1134/S1995080220040149#article-info

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

https://repository.kpfu.ru/eng/?p_id=237048&p_lang=2

Full metadata record

Field DC	Value	Language
dc.contributor.author	Khaliullin Samigulla Garifullovich	ru_RU
dc.date.accessioned	2020-01-01T00:00:00Z	ru_RU
dc.date.available	2020-01-01T00:00:00Z	ru_RU
dc.date.issued	2020	ru_RU
dc.identifier.citation	Haliullin, S.G. Ultraproducts for State-Spaces of C∗-Algebra and Radon Measures / Haliullin, S.G // Lobachevskii Journal of Mathematics. -2020. - 41(4). - P. 655–660	ru_RU
dc.identifier.uri	https://repository.kpfu.ru/eng/?p_id=237048&p_lang=2	ru_RU
dc.description.abstract	Lobachevskii Journal of Mathematics (international electronic journal)	ru_RU
dc.description.abstract	This paper deals with properties of the ultraproducts for various structures. We introduce and study the concept of the ergodic action of a group with respect to a normal state on an abelian von Neumann algebra. In particular, we provide an example showing that the ultraproduct of ergodic states, generally speaking, is not ergodic. The ultraproduct of the Radon measures on a compact convex subset of a locally convex space is also investigated in the paper. As is well-known, the study of the extreme points in the state set for a C∗−algebra is a very interesting problem in itself. Considering the ultraproducts of C∗-algebras and the states on these algebras, we get quite nontrivial results.	ru_RU
dc.language.iso	ru	ru_RU
dc.subject	ultraproduct	ru_RU
dc.subject	state-space	ru_RU
dc.subject	Radon measure	ru_RU
dc.title	Ultraproducts for State-Spaces of C∗-Algebra and Radon Measures	ru_RU
dc.type	Articles in international journals and collections	ru_RU