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dc.contributor.author | Hoa D. | |
dc.contributor.author | Tikhonov O. | |
dc.date.accessioned | 2018-09-18T20:16:42Z | |
dc.date.available | 2018-09-18T20:16:42Z | |
dc.date.issued | 2010 | |
dc.identifier.issn | 1066-369X | |
dc.identifier.uri | https://dspace.kpfu.ru/xmlui/handle/net/138218 | |
dc.description.abstract | We prove that a real function is operator monotone (operator convex) if the corresponding monotonicity (convexity) inequalities are valid for some normal state on the algebra of all bounded operators in an infinite-dimensional Hilbert space. We describe the class of convex operator functions with respect to a given von Neumann algebra in dependence of types of direct summands in this algebra. We prove that if a function from ℝ+ into ℝ+ is monotone with respect to a von Neumann algebra, then it is also operator monotone in the sense of the natural order on the set of positive self-adjoint operators affiliated with this algebra. © 2010 Allerton Press, Inc. | |
dc.relation.ispartofseries | Russian Mathematics | |
dc.subject | C*-algebra | |
dc.subject | operator convex function | |
dc.subject | operator monotone function | |
dc.subject | von Neumann algebra | |
dc.title | To the theory of operator monotone and operator convex functions | |
dc.type | Article | |
dc.relation.ispartofseries-issue | 3 | |
dc.relation.ispartofseries-volume | 54 | |
dc.collection | Публикации сотрудников КФУ | |
dc.relation.startpage | 7 | |
dc.source.id | SCOPUS1066369X-2010-54-3-SID78649557208 |