Some new refinements of numerical radius inequalities for Hilbert space operators

Abstract

Let $A$ and $B$ be bounded linear operators acting on a complex Hilbert space $\mathcal{H}$. In this paper, we define a new quantity $K(A)$ of $A$, which is less than the numerical raduis $w(A)$ of $A$. Based on this, we present some new refinements of the numerical radii of products $AB$, commutators $AB - BA$ and anticommutators $AB + BA$, which give an improvement to important results due to A. Abu-Omar and F. Kittaneh (Studia Math. 227 (2) (2015)).