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 ∈ B(H ) such that A, B are positive, we establish some numerical radius inequalities for A α XB α and A α XB 1−α (0 ≤ α ≤ 1) and Heinz means under mild conditions.

On the Dragomir Extension of Furuta's Inequality and Numerical Radius Inequalities

“…This result was also recently generalized by Sattari et al in [20] and Alomari in [3]. For more recent results about the numerical radius see the recent monograph study [5].…”

Refinements of some numerical radius inequalities for Hilbert space operators

“…This result was also recently generalized by Sattari et al in [29]. This work, is divided into four sections, after this introduction, in Section 2, we recall some well-known inequalities for bounded linear operators.…”

Numerical radius inequalities and its applications in estimation of zeros of polynomials

“…al. [16] proved that w r (B * A) ≤ 1 4 (AA * ) r + (BB * ) r + 1 2 w r (AB * ). When A = B * then w r (A 2 ) ≤ 1 4 (AA * ) r + (A * A) r + 1 2 w r (A 2 ).…”