KFU. Card publication. On convexity and compactness of operator ``intervals'' on Hilbert space

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ON CONVEXITY AND COMPACTNESS OF OPERATOR ``INTERVALS'' ON HILBERT SPACE

Form of presentation

Conference proceedings in Russian journals and collections

Year of publication

2018

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Authors, employees of KFU

Bikchentaev Ayrat Midkhatovich, author

Bibliographic description in the original language

Bikchentaev A.M., On convexity and compactness of operator «intervals'' on Hilbert space / A.M. Bikchentaev // Internat. sci. confer. «Infinite-dimensional analysis and control theory« dedicated to the centenary of the outstanding Russian mathematician S.V. Fomin (Moscow, January 29 - February 01, 2018). - M., 2018. - P. 4.

Annotation

Internat. sci. confer. "Infinite-dimensional analysis and control theory" dedicated to the centenary of the outstanding Russian mathematician S.V. Fomin (Moscow, January 29 - February 01, 2018)

Keywords

Hilbert space, von Neumann algebra, operator order, convexity, compactness

The name of the journal

Internat. sci. confer. "Infinite-dimensional analysis and control theory" dedicated to the centenary of the outstanding Russian mathematician S.V. Fomin (Moscow, January 29 - February 01, 2018)

On-line resource for training course

http://dspace.kpfu.ru/xmlui/bitstream/handle/net/118018/bikchentaev_abstract.pdf?sequence=1&isAllowed=y

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

https://repository.kpfu.ru/eng/?p_id=173945&p_lang=2

Resource files

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bikchentaev_abstract.pdf	0,06	pdf	show / download

Full metadata record

Field DC	Value	Language
dc.contributor.author	Bikchentaev Ayrat Midkhatovich	ru_RU
dc.date.accessioned	2018-01-01T00:00:00Z	ru_RU
dc.date.available	2018-01-01T00:00:00Z	ru_RU
dc.date.issued	2018	ru_RU
dc.identifier.citation	Bikchentaev A.M., On convexity and compactness of operator «intervals'' on Hilbert space / A.M. Bikchentaev // Internat. sci. confer. «Infinite-dimensional analysis and control theory« dedicated to the centenary of the outstanding Russian mathematician S.V. Fomin (Moscow, January 29 - February 01, 2018). - M., 2018. - P. 4.	ru_RU
dc.identifier.uri	https://repository.kpfu.ru/eng/?p_id=173945&p_lang=2	ru_RU
dc.description.abstract	Internat. sci. confer. "Infinite-dimensional analysis and control theory" dedicated to the centenary of the outstanding Russian mathematician S.V. Fomin (Moscow, January 29 - February 01, 2018)	ru_RU
dc.description.abstract	We consider a von Neumann algebra $M$ acting on a Hilbert space $H$. For a positive operator $X$ in $M$ we define the operator ``intervals'' $I_X=\{Y=Y^\in M: \; -X \leq Y \leq X \}$ and $L_X=\{Y \in M: \; \|Y\| \leq X \}$, where $\|Y\|=\sqrt{Y^Y}$. The properties of this operator ``intervals'' are investigated. We prove that a von Neumann algebra $M$ is Abelian if and only if $L_X$ is convex for all $X$ in $M$. We then show for $M=B(H)$, the algebra of all linear bounded operators on $H$, that the operator ``interval'' $I_X$ is compact if and only if an operator $X$ is compact.	ru_RU
dc.language.iso	ru	ru_RU
dc.subject	Hilbert space	ru_RU
dc.subject	von Neumann algebra	ru_RU
dc.subject	operator order	ru_RU
dc.subject	convexity	ru_RU
dc.subject	compactness	ru_RU
dc.title	On convexity and compactness of operator ``intervals'' on Hilbert space	ru_RU
dc.type	Conference proceedings in Russian journals and collections	ru_RU