A note on the relationship between spectral radius and norms of bounded linear operators

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Title:	A note on the relationship between spectral radius and norms of bounded linear operators
Author:	Munhoz Rodrigues, Hildebrando; Solà-Morales Rubió, Joan de
Other authors:	Universitat Politècnica de Catalunya. Departament de Matemàtica Aplicada I; Universitat Politècnica de Catalunya. EGSA - Equacions Diferencials, Geometria, Sistemes Dinàmics i de Control, i Aplicacions
Abstract:	Let X be a Banach space and L ( X ) be the Banach algebra of bounded operators on X . In this note we prove that if we have a compact subset K of a commutative sub-algebra of L ( X ), and given " > 0, then it is possible to de ne a new norm in X , equivalent to its given norm, in such a way that inside a neighborhood U " of this compact set in the sub- algebra, the norms of all the operators di er from their spectral radius in less than " . If X is a Hilbert space then it is possible to de ne this new norm as an Hilbertian norm.
Subject(s):	-Àrees temàtiques de la UPC::Matemàtiques i estadística -Banach spaces -Banach, Espais de -Àlgebra
Rights:	Attribution-NonCommercial-NoDerivs 3.0 Spain http://creativecommons.org/licenses/by-nc-nd/3.0/es/
Document type:	Article - Published version Article
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