Application of topological radicals to calculation of joint spectral radii

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dc.creatorShulman, Victor S.
dc.creatorTurovskii, Yuri V.
dc.date2008-05-02
dc.date.accessioned2026-07-07T09:36:39Z
dc.date.available2026-07-07T09:36:39Z
dc.descriptionIt is shown that the joint spectral radius $ρ(M)$ of a precompact family $M$ of operators on a Banach space $X$ is equal to the maximum of two numbers: the joint spectral radius $ρ_{e}(M)$ of the image of $M$ in the Calkin algebra and the Berger-Wang radius $r(M)$ defined by the formula \[ r(M)=\underset{n\to\infty}{\limsup}(\sup\left\{ρ(a):a\in M^{n}\right\} ^{1/n}) . \] Some more general Banach-algebraic results of this kind are also proved. The proofs are based on the study of special radicals on the class of Banach algebras.
dc.identifierhttps://arxiv.org/abs/0805.0209
dc.identifierhttp://arxiv.org/abs/0805.0209
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/160191
dc.subjectFunctional Analysis
dc.subjectSpectral Theory
dc.subject47D03; 46H05
dc.titleApplication of topological radicals to calculation of joint spectral radii
dc.typetext

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