KFU. Card publication. 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

Form of presentation

Articles in international journals and collections

Year of publication

2024

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Authors, employees of KFU

Bikchentaev Ayrat Midkhatovich, author

Tikhonov Oleg Evgenevich, author

Bibliographic description in the original language

A.M. Bikchentaev, O.E. Tikhonov, Continuity of operator functions in the topology of local convergence in measure // Proc. Steklov Inst. Math., 324 (2024), 44--52

Annotation

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.

Keywords

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

The name of the journal

PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS

On-line resource for training course

http://dspace.kpfu.ru/xmlui/bitstream/handle/net/184102/Psim044.pdf?sequence=1&isAllowed=y

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

https://repository.kpfu.ru/eng/?p_id=300181&p_lang=2

Resource files

File name	Size (MB)	Format
Psim044.pdf	1,58	pdf	show / download

Full metadata record

Field DC	Value	Language
dc.contributor.author	Bikchentaev Ayrat Midkhatovich	ru_RU
dc.contributor.author	Tikhonov Oleg Evgenevich	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 // Proc. Steklov Inst. Math., 324 (2024), 44--52	ru_RU
dc.identifier.uri	https://repository.kpfu.ru/eng/?p_id=300181&p_lang=2	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	Articles in international journals and collections	ru_RU