Spectral sets for locally bounded operators

2005/11/28 by Mirel Sorin Stoian, Stoian, Mirel Sorin
Mathematics · #FOS: Mathematics #Functional Analysis (math.FA) #math.FA

paper · pdf · doi:10.48550/arxiv.math/0511671

arxiv created 2005/11/28 · arxiv updated 2009/12/01

Abstract

In this paper we present some spectral property for quotient bounded operators and locally bounded operators on locally convex spaces. We introduce the spectral radius of a quotient bounded operator and we show that the Gelfand formula for spectral radius and Newmann series have the same properties like in Banach spaces. Moreover, the geometrical radius of the spectrum is equal with the spectral radius. Using definitions of V.Troitsky we prove that the spectral set of a quotient bounded operator is compact set.

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