Monotonicity properties for joint and generalized spectral radius and their essential versions of weighted geometric symmetrizations

TL;DR

This paper establishes new monotonicity properties for spectral radii and their essential versions in the context of weighted geometric symmetrizations of positive kernel operators, with novel results even in finite dimensions.

Contribution

It introduces new monotonicity properties for spectral radii and their essential versions, expanding understanding in both infinite and finite-dimensional cases.

Findings

New monotonicity properties proved for spectral radii.

Properties are novel even in finite-dimensional settings.

Results applicable to weighted geometric symmetrizations of positive kernel operators.

Abstract

We prove new monotonicity properties for joint and generalized spectral radius and their essential versions of weighted geometric symmetrizations of bounded sets of positive kernel operators on $L^2$. To our knowledge, several proved properties are new even in the finite dimensional case.