JENSEN TYPE WEIGHTED INEQUALITIES FOR FUNCTIONS OF SELFADJOINT AND UNITARY OPERATORS

Abstract

On making use of the spectral representations in terms of the Riemann-Stieltjes integral for the selfadjoint and unitary operators in Hilbert spaces we establish here some weighted inequalities of Jensen’s type for convex, square-convex and Arg-square-convex functions.  Some applications for simple functions of operators that belong to those classes are also provided.