Inequalities and equalities on the joint and generalized spectral and essential spectral radius of the Hadamard geometric mean of bounded sets of positive kernel operators

TL;DR

This paper establishes new inequalities and equalities for spectral radii of Hadamard geometric means of positive kernel operators, extending recent results and covering both Banach function spaces and nonnegative matrices.

Contribution

It introduces novel inequalities and equalities for spectral radii of Hadamard geometric means of positive kernel operators, broadening existing theoretical frameworks.

Findings

New inequalities for spectral radii of Hadamard geometric means.

Equalities for joint and essential spectral radii.

Extensions to nonnegative matrices on Banach sequences.

Abstract

We prove new inequalities and equalities for the generalized and the joint spectral radius (and their essential versions) of Hadamard (Schur) geometric means of bounded sets of positive kernel operators on Banach function spaces. In the case of nonnegative matrices that define operators on Banach sequences we obtain additional results. Our results extend results of several authors that appeared relatively recently.