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Around Operator Monotone Functions

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Abstract

We show that the symmetrized product AB + BA of two positive operators A and B is positive if and only if \({f(A+B)\leq f(A)+f(B)}\) for all non-negative operator monotone functions f on [0,∞) and deduce an operator inequality. We also give a necessary and sufficient condition for that the composition \({f \circ g}\) of an operator convex function f on [0,∞) and a non-negative operator monotone function g on an interval (a, b) is operator monotone and present some applications.

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Authors and Affiliations

  1. Department of Pure Mathematics, Center of Excellence in Analysis on Algebraic Structures (CEAAS), Ferdowsi University of Mashhad, P. O. Box 1159, 91775, Mashhad, Iran

    Mohammad Sal Moslehian & Hamed Najafi

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  1. Mohammad Sal Moslehian
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  2. Hamed Najafi
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Correspondence to Hamed Najafi.

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Moslehian, M.S., Najafi, H. Around Operator Monotone Functions. Integr. Equ. Oper. Theory 71, 575–582 (2011). https://doi.org/10.1007/s00020-011-1921-0

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  • DOI: https://doi.org/10.1007/s00020-011-1921-0

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