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

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.

This preprint is the replacement of the arxiv preprint of the article "Monotonicity properties of weighted geometric symmetrizations'' that has been published (open access) in Journal of Mathematical Inequalities, 2024, doi:10.7153/jmi-2024-18-87. arXiv admin note: substantial text overlap with arXiv:2202.02325, arXiv:2402.04265, arXiv:1805.09680, arXiv:2107.09459, arXiv:1612.01765