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International Journal of Mathematics and Mathematical Sciences
Volume 20, Issue 3, Pages 585-588
http://dx.doi.org/10.1155/S0161171297000793

A formula to calculate the spectral radius of a compact linear operator

Escuela de Ciencias Físico-Matemáticas, Universidad Michoacana de San Nicolás de Hidalgo, Edificio B. Ciudad Universitaria, Morelia, Michoacán 58060, Mexico

Received 3 April 1995; Revised 21 September 1995

Copyright © 1997 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

There is a formula (Gelfand's formula) to find the spectral radius of a linear operator defined on a Banach space. That formula does not apply even in normed spaces which are not complete. In this paper we show a formula to find the spectral radius of any linear and compact operator T defined on a complete topological vector space, locally convex. We also show an easy way to find a non-trivial T-invariant closed subspace in terms of Minkowski functional.