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.

On further refinements for Young inequalities

“…In our previous work [3], we gave new sharp inequalities for reverse Young inequalities. In this section, we firstly give new sharp inequalities for Young inequalities, as limited cases in the first inequalities both (i) and (ii) of the following theorem.…”

“…In [3,5] we proved some sharp multiplicative reverses of Young's inequality. In this brief note, as the continuation of our previous works, we establish sharp bounds for the arithmetic, geometric and harmonic mean inequalities.…”

Further inequalities for the numerical radius of Hilbert space operators

“…On account of assumptions on h, we can write Our aim in the next result is to improve (1.6) under some mild conditions. To do this end, we need the following refinement of arithmetic-geometric mean inequality [9,10]. Proof…”

On some general inequalities related to operator AM-GM inequality

“…The problem of squaring operator inequalities has been studied extensively in the literature. We refer the reader to [4,[8][9][10]12] as sample of this work.…”