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

Fernando Garibay Bonales and Rigoberto Vera Mendoza

 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

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.