Some Inequalities for Power Series of Selfadjoint Operators in Hilbert Spaces Via Wielandt and Reverses of Schwarz Inequalities

Abstract

In this paper we obtain some operator inequalities for functions defined by power series with complex coefficients and, more specifically, with nonnegative coefficients. In order to obtain these inequalities the classical Wielandt and some reverses of the Schwarz inequality for vectors in inner product spaces are utilized. Natural applications for some elementary functions of interest are also provided.