New sharp inequalities for operator means

Abstract

New sharp multiplicative reverses of the operator means inequalities are presented, with a simple discussion of squaring an operator inequality. As a direct consequence, we extend the operator Pólya-Szegö inequality to arbitrary operator means. Furthermore, we obtain some new lower and upper bounds for the Tsallis relative operator entropy, operator monotone functions and positive linear maps.

to appear in Linear and Multilinear Algebra

References in corpus (2)

• Operator log-convex functions and operator means
• On an operator Kantorovich inequality for positive linear maps