International Journal of Mathematics and Mathematical Sciences
Volume 20 (1997), Issue 3, Pages 585-588
doi: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 58060, Michoacán, Mexico
Received 3 April 1995; Revised 21 September 1995
Copyright © 1997 Fernando Garibay Bonales and Rigoberto Vera Mendoza. 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.