Kantorovich Type Integral Inequalities for Tensor Product of Continuous Fields of Hilbert Space Operators

TL;DR

This paper develops Kantorovich type integral inequalities for tensor products of continuous operator fields on Hilbert spaces, including operator mean versions and generalizations of Gruss inequalities, extending classical inequalities in operator theory.

Contribution

It introduces new Kantorovich integral inequalities involving tensor products and operator means, generalizing existing inequalities and including discrete cases.

Findings

Derived Kantorovich integral inequalities for tensor product operators

Extended inequalities to include operator means

Generalized Gruss-type inequalities for operators

Abstract

This paper presents a number of Kantorovich type integral inequalities involving tensor products of continuous fields of bounded linear operators on a Hilbert space. Kantorovich type inequality in which the product is replaced by an operator mean is also considered. Such inequalities include discrete inequalities as special cases. Moreover, some generalizations of an additive Gruss integral inequality for operators are obtained.