An inequality for tensor product of positive operators and its applications

TL;DR

This paper introduces a new inequality for tensor products of positive operators on Hilbert spaces and applies it to derive various matrix inequalities involving determinants and permanents.

Contribution

It presents a novel inequality for tensor products of positive operators and uses multilinear methods to obtain related matrix inequalities.

Findings

Derived a new inequality for tensor products of positive operators.

Applied the inequality to obtain matrix inequalities involving determinants and permanents.

Extended the inequality to induced operators and generalized matrix functions.

Abstract

We present an inequality for tensor product of positive operators on Hilbert spaces by considering the tensor product of operators as words on certain alphabets (i.e., a set of letters). As applications of the operator inequality and by a multilinear approach, we show some matrix inequalities concerning induced operators and generalized matrix functions (including determinants and permanents as special cases).