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

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