КФУ. Карточка публикации. Continuity of operator functions in the topology of local convergence in measure

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CONTINUITY OF OPERATOR FUNCTIONS IN THE TOPOLOGY OF LOCAL CONVERGENCE IN MEASURE

Форма представления

Статьи в зарубежных журналах и сборниках

Год публикации

2024

Язык

английский

Авторы, сотрудники КФУ

Бикчентаев Айрат Мидхатович, автор

Библиографическое описание на языке оригинала

A.M. Bikchentaev, O.E. Tikhonov, Continuity of operator functions in the topology of local convergence in measure

Аннотация

Let a von Neumann algebra M of operators act on a Hilbert space H , τ be a faithful normal semifinite trace on M. Let tτl be the topology of τ-local convergence in measure on the *-algebra S(M,τ) of all τ -measurable operators. We prove the tτl-continuity of the involution on the set of all normal operators in S(M,τ). We investigate the tτl -continuity of operator functions on S(M,τ) . We show that the mapping A↦|A| is tτl-continuous on the set of all partial isometries in M.

Ключевые слова

Hilbert space, linear operator, von Neumann algebra, normal trace, measurable operator, local convergence in measure, continuity of operator functions

Название журнала

PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS

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https://repository.kpfu.ru/?p_id=300181

Полная запись метаданных

Поле DC	Значение	Язык
dc.contributor.author	Бикчентаев Айрат Мидхатович	ru_RU
dc.date.accessioned	2024-01-01T00:00:00Z	ru_RU
dc.date.available	2024-01-01T00:00:00Z	ru_RU
dc.date.issued	2024	ru_RU
dc.identifier.citation	A.M. Bikchentaev, O.E. Tikhonov, Continuity of operator functions in the topology of local convergence in measure	ru_RU
dc.identifier.uri	https://repository.kpfu.ru/?p_id=300181	ru_RU
dc.description.abstract	PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS	ru_RU
dc.description.abstract	Let a von Neumann algebra M of operators act on a Hilbert space H , τ be a faithful normal semifinite trace on M. Let tτl be the topology of τ-local convergence in measure on the *-algebra S(M,τ) of all τ -measurable operators. We prove the tτl-continuity of the involution on the set of all normal operators in S(M,τ). We investigate the tτl -continuity of operator functions on S(M,τ) . We show that the mapping A↦\|A\| is tτl-continuous on the set of all partial isometries in M.	ru_RU
dc.language.iso	ru	ru_RU
dc.subject	Hilbert space	ru_RU
dc.subject	linear operator	ru_RU
dc.subject	von Neumann algebra	ru_RU
dc.subject	normal trace	ru_RU
dc.subject	measurable operator	ru_RU
dc.subject	local convergence in measure	ru_RU
dc.subject	continuity of operator functions	ru_RU
dc.title	Continuity of operator functions in the topology of local convergence in measure	ru_RU
dc.type	Статьи в зарубежных журналах и сборниках	ru_RU