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

A formula for the inner spectral radius

1School of Mathematical Science, Isfahan University of Technology, Isfahan 84156, Iran
2Department of Mathematics and Statistics, University of Regina, Regina, Saskatchewan S4S 0A2, Canada

Received 3 November 2003

Copyright © 2004 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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.