International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 61-64, Pages 3285-3290
doi:10.1155/S0161171204311063

A formula for the inner spectral radius

Abstract

This note presents an asymptotic formula for the minimum of the moduli of the elements in the spectrum of a bounded linear operator acting on Banach space X. This minimum moduli is called the inner spectral radius, and the formula established herein is an analogue of Gelfand's spectral radius formula.