Interpolating between the Arithmetic-Geometric Mean and Cauchy-Schwarz matrix norm inequalities

TL;DR

This paper introduces a new inequality for unitarily invariant norms that bridges the gap between the Arithmetic-Geometric Mean and Cauchy-Schwarz inequalities, expanding the theoretical understanding of matrix norm relations.

Contribution

It presents a novel interpolating inequality for unitarily invariant norms, connecting two fundamental matrix inequalities in a unified framework.

Findings

Established a new inequality bridging AM-GM and Cauchy-Schwarz

Enhanced understanding of matrix norm relationships

Potential applications in matrix analysis and quantum information

Abstract

We prove an inequality for unitarily invariant norms that interpolates between the Arithmetic-Geometric Mean inequality and the Cauchy-Schwarz inequality.