Sequences of bounds for the spectral radius of a positive operator

Roman Drnovšek

doi:10.1016/j.laa.2019.03.024

paper

Sequences of bounds for the spectral radius of a positive operator

arXiv:1904.01835 · doi:10.1016/j.laa.2019.03.024

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, Taşçi 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.