Hadamard weighted geometric mean inequalities for the spectral and essential spectral radius of positive operators on Banach function and sequence spaces

TL;DR

This paper establishes new inequalities relating spectral and numerical properties of Hadamard weighted geometric means of positive operators on Banach spaces, with some results novel even in finite dimensions.

Contribution

It introduces new inequalities for spectral and essential spectral radii of Hadamard weighted geometric means of positive operators, expanding understanding in both infinite and finite dimensional cases.

Findings

New inequalities for spectral radius and essential spectral radius

Results applicable to Banach function and sequence spaces

Some inequalities are novel even in finite dimensions

Abstract

We prove new inequalities for the spectral radius, essential spectral radius, operator norm, measure of noncompactness and numerical radius of Hadamard weighted geometric means of positive kernel operators on Banach function and sequence spaces. Several inequalities appear to be new even in the finite dimensional case.