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

• Main Authors: Fernando Garibay Bonales, Rigoberto Vera Mendoza
• Format: Article
• Language: English
• Published: Hindawi Limited 1997-01-01
• Series: International Journal of Mathematics and Mathematical Sciences
• Subjects: compact linear operator; spectral radius; locally convex topological linear space; invariant subspace; nets; ultimately bounded nets.
• Online Access: http://dx.doi.org/10.1155/S0161171297000793
• ISSN: 0161-1712; 1687-0425

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.