This article is cited in 13 papers

Topological Radicals and Joint Spectral Radius

Yu. V. Turovskii^a, V. S. Shulman<sup>b

a</sup> Institute of Mathematics and Mechanics, Azerbaijan National Academy of Sciences, Baku
^b Vologda State Technical University

Abstract: It is shown that the joint spectral radius $\rho(M)$ of a precompact set $M$ of operators on a Banach space equals the maximum of two numbers, the joint spectral radius $\rho_{e}(M)$ of the image of $M$ in the Calkin algebra and the BW-radius $r(M)$. Similar results related to general normed algebras are also obtained. The proofs are based on the theory of topological radicals of normed algebras.

Keywords: joint spectral radius, the Berger–Wang formula, topological radical, invariant subspace.

UDC: 517.986.22

Received: 20.11.2010

DOI: 10.4213/faa3089

 English version: Functional Analysis and Its Applications, 2012, 46:4, 287–304

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