Operator inequalities via accretive transforms

TL;DR

This paper introduces new operator inequalities using accretive transforms, establishing relations among various operator moduli and extending numerical radius inequalities in complex Hilbert spaces.

Contribution

It presents novel inequalities for bounded linear operators based on the transform $C_{M,m}(A)$, advancing the understanding of operator relations and numerical radius bounds.

Findings

New inequalities relating $|A|,|A^*|,| ext{Re}A|,| ext{Im}A|$

Extended numerical radius inequalities

Enhanced bounds for operator analysis

Abstract

In this article, we employ certain properties of the transform $C_{M,m}(A)=(MI-A^*)(A-mI)$ to obtain new inequalities for the bounded linear operator $A$ on a complex Hilbert space $\mathcal{H}$. In particular, we obtain new relations among $|A|,|A^*|,|\mathfrak{R}A|$ and $|\mathfrak{I}A|$. Further numerical radius inequalities that extend some known inequalities will be presented too.