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On convexity and compactness of operator ``intervals'' on Hilbert space

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dc.contributor Казанский федеральный университет
dc.contributor.author Bikchentaev Airat Midkhatovich
dc.date.accessioned 2018-02-06T13:33:28Z
dc.date.available 2018-02-06T13:33:28Z
dc.date.issued 2018
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.
dc.identifier.uri http://dspace.kpfu.ru/xmlui/handle/net/118018
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.
dc.language.iso en
dc.relation.ispartofseries Internat. sci. confer. andquot;Infinite-dimensional analysis and control theoryandquot; dedicated to the centenary of the outstanding Russian mathematician S.V. Fomin (Moscow, January 29 - February 01, 2018)
dc.rights открытый доступ
dc.subject Hilbert space
dc.subject von Neumann algebra
dc.subject operator order
dc.subject convexity
dc.subject compactness
dc.subject.other Математика
dc.title On convexity and compactness of operator ``intervals'' on Hilbert space
dc.type Thesis
dc.contributor.org Институт вычислительной математики и информационных технологий
dc.description.pages
dc.pub-id 173945


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