КФУ. Карточка публикации. Ultraproducts for State-Spaces of C∗-Algebra and Radon Measures

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

Форма представления

Статьи в зарубежных журналах и сборниках

Год публикации

2020

Язык

русский

Авторы, сотрудники КФУ

Халиуллин Самигулла Гарифуллович, автор

Библиографическое описание на языке оригинала

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

Аннотация

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.

Ключевые слова

ultraproduct, state-space, Radon measure

Название журнала

Lobachevskii Journal of Mathematics (international electronic journal)

URL

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

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https://repository.kpfu.ru/?p_id=237048

Полная запись метаданных

Поле DC	Значение	Язык
dc.contributor.author	Халиуллин Самигулла Гарифуллович	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/?p_id=237048	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	Статьи в зарубежных журналах и сборниках	ru_RU