KFU. Card publication. 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

Form of presentation

Articles in international journals and collections

Year of publication

2017

Язык

английский

Authors, employees of KFU

Novikov Andrey Andreevich, author

Bibliographic description in the original language

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

Annotation

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.

Keywords

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

The name of the journal

POSITIVITY

URL

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

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

https://repository.kpfu.ru/eng/?p_id=138915&p_lang=2

Full metadata record

Field DC	Value	Language
dc.contributor.author	Novikov Andrey Andreevich	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/eng/?p_id=138915&p_lang=2	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	Articles in international journals and collections	ru_RU