Abstract
ABSTRACT A continuous function is called operator Schur convex, if f is symmetric, namely for all x, and in the operator order, for all and where is the convex set of all selfadjoint operators on Hilbert space H with spectra in I. In this paper we investigate the main properties of such functions, establish some integral inequalities of Hermite–Hadamard, Čebyšev and Grüss' type and give some general classes of examples of operator Schur-convex functions.
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