Further numerical radius inequalities

TL;DR

This paper introduces new inequalities for the numerical radius of operator products and the generalized Aluthge transform, providing upper bounds and generalizations of existing results in operator theory.

Contribution

It presents novel inequalities involving the numerical radius, including bounds for products of operators and the generalized Aluthge transform, extending prior research in the field.

Findings

Derived upper bounds for $\omega(ABC+DEF)$ using Buzano inequality

Generalized existing results on numerical radius inequalities

Established inequalities involving the generalized Aluthge transform

Abstract

In this article, we present some new inequalities for the numerical radius of products of Hilbert space operators and the generalized Aluthge transform. In particular, we show some upper bounds for $\omega(ABC+DEF)$ using the celebrated Buzano inequality, then some consequences that generalize some results from the literature are discussed. After that, inequalities that involve the generalized Aluthge transform are shown using some known bounds for the numerical radius of the product of two operators.