Some results on singular value inequalities of compact operators in Hilbert space

TL;DR

This paper establishes new singular value inequalities for sums and products of compact operators in Hilbert space, extending previous results and demonstrating applications of these inequalities.

Contribution

It introduces generalized singular value inequalities for compact operators, broadening the scope of existing operator inequalities and providing practical applications.

Findings

New inequalities for sums of compact operators

Generalized inequalities for operator products

Applications demonstrating the usefulness of the inequalities

Abstract

We prove several singular value inequalities for sum and product of compact operators in Hilbert space. Some of our results generalize the previous inequalities for operators. Also, applications of some inequalities are given.