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On the extreme points of sets in spaces of operators and spaces of states

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dc.contributor Казанский федеральный университет
dc.contributor.author Amosov Grigoriy Gennadevich
dc.contributor.author Bikchentaev Airat Midkhatovich
dc.contributor.author Sakbaev Vsevolod Zhanovich
dc.date.accessioned 2024-07-16T06:23:31Z
dc.date.available 2024-07-16T06:23:31Z
dc.date.issued 2024
dc.identifier.citation Amosov G.G., Bikchentaev A.M., Sakbaev V. Zh. On Extreme Points of Sets in Operator Spaces and State Spaces / G.G. Amosov, A.M. Bikchentaev, V. Zh. Sakbaev // Proc. Steklov Inst. Math. - 2024. - 324. - P. 4--17.
dc.identifier.uri https://dspace.kpfu.ru/xmlui/handle/net/184103
dc.description.abstract A representation of the set of quantum states by barycenters of non-negative normalized finite additive measures on a unit sphere of Hilbert space H is obtained. In terms of the properties of a measure on a unit sphere of space H, the conditions for its barycenter to belong to the set of extreme points of the set of quantum states and to the set of normal states are derived. A characterization of the unitary elements of the unital C∗-algebra in terms of extreme points is obtained. The extreme points of the unit ball E1 of the normalized ideal space of operators ⟨E,∥⋅∥E⟩ on H are investigated. If U∈extr(E1) for some unitary operator U∈B(H), then V∈extr(E1) for all unitary operators V∈B(H). Quantum correlations corresponding to the singular state on the algebra of all bounded operators in a Hilbert space are constructed.
dc.language.iso en
dc.relation.ispartofseries PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS
dc.rights открытый доступ
dc.subject Hilbert space
dc.subject linear operator
dc.subject C*-algebra
dc.subject von Neumann algebra
dc.subject normed ideal space of operators
dc.subject quantum state
dc.subject finite-additive measure
dc.subject baricenter
dc.subject extemal point
dc.subject quantum korrelations
dc.subject generated by states
dc.subject.other Математика
dc.title On the extreme points of sets in spaces of operators and spaces of states
dc.type Article
dc.contributor.org Институт математики и механики им. Н.И. Лобачевского
dc.description.pages 4-17
dc.relation.ispartofseries-volume 324
dc.pub-id 300182


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