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Commutators and hyponormal operators on a Hilbert space

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dc.contributor Казанский федеральный университет
dc.contributor.author Akhmadiev Marat Gabdelbyarovich
dc.contributor.author Alhasan Khasan
dc.contributor.author Bikchentaev Airat Midkhatovich
dc.contributor.author Ivanshin Petr Nikolaevich
dc.date.accessioned 2023-07-07T12:54:38Z
dc.date.available 2023-07-07T12:54:38Z
dc.date.issued 2023
dc.identifier.citation M. Akhmadiev. Commutators and hyponormal operators on a Hilbert space / M. Akhmadiev, H. Alhasan, A. Bikchentaev, P. Ivanshin // J. Iran. Math. Soc. 2023. Vol. 4. № 1. P 67--78.
dc.identifier.uri https://dspace.kpfu.ru/xmlui/handle/net/176401
dc.description.abstract Let H be an innite-dimensional Hilbert space over the field C, B(H) be the ∗-algebra of all linear bounded operators on H. An operator A ∈ B(H) is a commutator, if A = [S, T ] = ST - T S for some S, T ∈ B(H). Let X, Y ∈ B(H) and X ≥ 0. If the operator XY is a non-commutator, then X^pY X^{1-p} is a non-commutator for every 0 ( p ( 1. Let A ∈ B(H) be p-hyponormal for some 0 ( p ≤ 1. If |A^∗|^r is a non-commutator for some r ) 0, then |A|^q is a non-commutator for every q ) 0. Let H be separable and A ∈ B(H) be a non-commutator. If A is hyponormal (or cohyponormal), then A is normal. We also present results in the case of a finite-dimensional Hilbert space.
dc.language.iso en
dc.relation.ispartofseries Journal of the Iranian Mathematical Society
dc.rights открытый доступ
dc.subject Hilbert space
dc.subject linear operator
dc.subject commutator
dc.subject hyponormal operator
dc.subject trace
dc.subject.other Математика
dc.title Commutators and hyponormal operators on a Hilbert space
dc.type Article
dc.contributor.org Институт математики и механики им. Н.И. Лобачевского
dc.description.pages 67-78
dc.relation.ispartofseries-issue 1
dc.relation.ispartofseries-volume 4
dc.pub-id 283141


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