To the theory of operator monotone and operator convex functions

Autor:	O. E. Tikhonov, Dinh Trung Hoa
Rok vydání:	2010
Předmět:	Discrete mathematics Pseudo-monotone operator Von Neumann's theorem Operator algebra General Mathematics Operator theory Reflexive operator algebra Compact operator Affiliated operator Mathematics Quasinormal operator
Zdroj:	Russian Mathematics. 54:7-11
ISSN:	1934-810X 1066-369X
DOI:	10.3103/s1066369x10030023
Popis:	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.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::cc1f22d61d57dfe5a56fb06f013530d5 https://doi.org/10.3103/s1066369x10030023 Zobrazit plný text záznamu Full text from SpringerLink