Some Inequalities for Power Series of Selfadjoint Operators in Hilbert Spaces via Reverses of the Schwarz Inequality

摘要

In this paper we obtain some operator inequalities for functions\uddefined by power series with real coefficients and, more specifically, with non-\udnegative coefficients. In order to obtain these inequalities some recent reverses\udof the Schwarz inequality for vectors in inner product spaces are utilized. Natural applications for some elementary functions of interest are also provided.