International Journal of Mathematics and Mathematical Sciences
Volume 2004 (2004), Issue 61, Pages 3285-3290
doi: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 S4S 0A2, Saskatchewan, Canada
Received 3 November 2003
Copyright © 2004 S. Mahmoud Manjegani. 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.