# Sequences of bounds for the spectral radius of a positive operator

## TL;DR

This paper extends sequences of bounds for the spectral radius from nonnegative matrices to positive operators on L^2-spaces, providing a broader theoretical framework for spectral analysis.

## Contribution

It generalizes existing bounds for the spectral radius from matrices to positive operators on L^2-spaces, enhancing the theoretical understanding.

## Key findings

- Sequences of bounds are extended to positive operators on L^2-spaces.
- Theoretical framework for spectral radius bounds is broadened.
- Results unify matrix and operator spectral analysis.

## Abstract

In 1992, Szyld provided a sequence of lower bounds for the spectral radius of a nonnegative matrix $A$, based on the geometric symmetrization of powers of $A$. In 1998, Ta\c{s}\c{c}i and Kirkland proved a companion result by giving a sequence of upper bounds for the spectral radius of $A$, based on the arithmetic symmetrization of powers of $A$. In this note, we extend both results to positive operators on $L^2$-spaces.