Operator inequalities via the triangle inequality

TL;DR

This paper refines the triangle inequality for complex numbers using convex analysis and applies these improvements to derive new operator inequalities, including bounds on numerical radius and operator means.

Contribution

It introduces a novel refinement of the triangle inequality for complex numbers and applies this to establish new operator inequalities.

Findings

Refined triangle inequality for complex numbers.

New bounds on numerical radius of operators.

Enhanced operator mean inequalities.

Abstract

This article improves the triangle inequality for complex numbers, using the Hermite-Hadamard inequality for convex functions. Then, applications of the obtained refinement are presented to include some operator inequalities. The operator applications include numerical radius inequalities and operator mean inequalities.