New log-majorization results concerning eigenvalues and singular values and a complement of a norm inequality

TL;DR

This paper introduces new log-majorization results for eigenvalues and singular values, extending previous conjectures and providing a complement to a norm inequality related to unitarily invariant norms.

Contribution

It generalizes existing results on eigenvalue and singular value inequalities and offers a new complement to a conjectured unitarily invariant norm inequality.

Findings

New log-majorization results for eigenvalues and singular values

A proven complement to a conjectured norm inequality

Extension of previous conjectures and open questions

Abstract

The purpose of this paper is to establish new log-majorization results concerning eigenvalues and singular values which generalize some previous work related to a conjecture and an open question which were presented by R. Lemos and G. Soares in \cite{lemos}. In addition, we present a complement of a unitarily invariant norm inequality which was conjectured by R. Bhatia, Y. Lim and T. Yamazaki in \cite{Bhatia2}, and recently proved by T.H. Dinh, R. Dumitru and J.A. Franco in \cite{Dinh} for the Schatten p-norm with $1\leq p\leq \infty$.