Some inequalities for power series of selfadjoint operatorsin Hilbert spaces via reverses of the Schwarz inequality

摘要

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