Some generalized numerical radius inequalities for Hilbert space operators

Abstract

We generalize several inequalities involving powers of the numerical radius for product of two operators acting on a Hilbert space. For any $A,B,X\in \mathbb{B}(\mathcal{H})$ such that $A,B$ are positive, we establish some numerical radius inequalities for $A^{\alpha }X{B}^{\alpha }$ and $A^{\alpha }X{B}^{1-\alpha }(0\le \alpha \le 1)$ and Heinz means under mild conditions.

12 pages, to appear in Linear Algebra Appl. (LAA)

References in corpus (1)

• Further refinements of the Heinz inequality