Operator Inequalities of the Jensen, _eby_ev and Grüss Type

The main aim of this book is to present recent results concerning inequalities of the Jensen, AiebyA!ev and Gruss type for continuous functions of bounded selfadjoint operators on complex Hilbert spaces. In the introductory chapter, the author portrays fundamental facts concerning bounded selfadjoint operators on complex Hilbert spaces. The generalized Schwarz's inequality for positive selfadjoint operators as well as some results for the spectrum of this class of operators are presented. This text introduces the reader to the fundamental results for polynomials in a linear operator, continuou