КФУ. Карточка публикации. L1-space for a positive operator affiliated with von Neumann algebra

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L1-SPACE FOR A POSITIVE OPERATOR AFFILIATED WITH VON NEUMANN ALGEBRA

Форма представления

Статьи в зарубежных журналах и сборниках

Год публикации

2017

Язык

английский

Авторы, сотрудники КФУ

Новиков Андрей Андреевич, автор

Библиографическое описание на языке оригинала

Novikov A., L1-space for a positive operator affiliated with von Neumann algebra//Positivity. - 2017. - Vol 21., Is. 1. - P.359-375.

Аннотация

In this paper we suggest an approach for constructing an L1-type space for a positive selfadjoint operator affiliated with von Neumann algebra. For such operator we introduce a seminorm, and prove that it is a norm if and only if the operator is injective. For this norm we construct an L1-type space as the complition of the space of hermitian ultraweakly continuous linear functionals on von Neumann algebra, and represent L1-type space as a space of continuous linear functionals on the space of special sesquilinear forms. Also, we prove that L1-type space is isometrically isomorphic to the predual of von Neumann algebra in a natural way. We give a small list of alternate definitions of the seminorm, and a special definition for the case of semifinite von Neumann algebra, in particular. We study order properties of L1-type space, and demonstrate the connection between semifinite normal weights and positive elements of this space.

Ключевые слова

Operator algebra, Von Neumann algebra, C*-algebra, Noncommutative integration, L1-space, Positive operator, Semifinite normal weight, Unbounded operator

Название журнала

POSITIVITY

URL

http://link.springer.com/article/10.1007/s11117-016-0422-4

Пожалуйста, используйте этот идентификатор, чтобы цитировать или ссылаться на эту карточку

https://repository.kpfu.ru/?p_id=138915

Полная запись метаданных

Поле DC	Значение	Язык
dc.contributor.author	Новиков Андрей Андреевич	ru_RU
dc.date.accessioned	2017-01-01T00:00:00Z	ru_RU
dc.date.available	2017-01-01T00:00:00Z	ru_RU
dc.date.issued	2017	ru_RU
dc.identifier.citation	Novikov A., L1-space for a positive operator affiliated with von Neumann algebra//Positivity. - 2017. - Vol 21., Is. 1. - P.359-375.	ru_RU
dc.identifier.uri	https://repository.kpfu.ru/?p_id=138915	ru_RU
dc.description.abstract	POSITIVITY	ru_RU
dc.description.abstract	In this paper we suggest an approach for constructing an L1-type space for a positive selfadjoint operator affiliated with von Neumann algebra. For such operator we introduce a seminorm, and prove that it is a norm if and only if the operator is injective. For this norm we construct an L1-type space as the complition of the space of hermitian ultraweakly continuous linear functionals on von Neumann algebra, and represent L1-type space as a space of continuous linear functionals on the space of special sesquilinear forms. Also, we prove that L1-type space is isometrically isomorphic to the predual of von Neumann algebra in a natural way. We give a small list of alternate definitions of the seminorm, and a special definition for the case of semifinite von Neumann algebra, in particular. We study order properties of L1-type space, and demonstrate the connection between semifinite normal weights and positive elements of this space.	ru_RU
dc.language.iso	ru	ru_RU
dc.subject	Operator algebra	ru_RU
dc.subject	Von Neumann algebra	ru_RU
dc.subject	C*-algebra	ru_RU
dc.subject	Noncommutative integration	ru_RU
dc.subject	L1-space	ru_RU
dc.subject	Positive operator	ru_RU
dc.subject	Semifinite normal weight	ru_RU
dc.subject	Unbounded operator	ru_RU
dc.title	L1-space for a positive operator affiliated with von Neumann algebra	ru_RU
dc.type	Статьи в зарубежных журналах и сборниках	ru_RU