Some results on singular value inequalities of normal operators

TL;DR

This paper extends a classical inequality involving complex numbers to the operator setting, providing new bounds for normal operators and enriching the understanding of their singular value properties.

Contribution

It introduces an operator version of a known complex number inequality and derives new results specifically for normal operators.

Findings

Established an operator analogue of the complex number inequality.

Derived bounds for the singular values of normal operators.

Enhanced the theoretical understanding of normal operator inequalities.

Abstract

Let $x=a+ib$ be a complex number, so we have the following inequality $$(1/\sqrt{2})|a+b|\leq |x|\leq |a|+|b|$$ We give an operator version of above inequality. Also we obtain some results for normal operators.