Norm and numerical radius inequalities for operator matrices

TL;DR

This paper investigates properties of operator matrices, providing new bounds for their norms and numerical radii, especially focusing on matrices with positive real and imaginary parts, enhancing understanding of their behavior.

Contribution

It introduces novel estimates for operator norms and numerical radii, and analyzes operator matrices with positive real and imaginary parts, offering sharper bounds than existing results.

Findings

New bounds for operator norms and numerical radii.

Analysis of operator matrices with positive real and imaginary parts.

Sharper bounds for specific classes of operator matrices.

Abstract

Operator matrices have played a significant role in studying Hilbert space operators. In this paper, we discuss further properties of operator matrices and present new estimates for the operator norms and numerical radii of such operators. Moreover, operator matrices whose real and imaginary parts are positive will be discussed, and sharper bounds will be shown for such class.