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Currently displaying 1 – 3 of 3

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Formulae for joint spectral radii of sets of operators

Victor S. Shulman; Yuriĭ V. Turovskii — 2002

Studia Mathematica

The formula $ϱ (M) = m a x ϱ_{χ} (M), r (M)$ is proved for precompact sets M of weakly compact operators on a Banach space. Here ϱ(M) is the joint spectral radius (the Rota-Strang radius), $ϱ_{χ} (M)$ is the Hausdorff spectral radius (connected with the Hausdorff measure of noncompactness) and r(M) is the Berger-Wang radius.

On the Kleinecke-Shirokov Theorem for families of derivations

Victor S. Shulman; Yuriĭ V. Turovskii — 2002

Studia Mathematica

It is proved that Riesz elements in the intersection of the kernel and the closure of the image of a family of derivations on a Banach algebra are quasinilpotent. Some related results are obtained.

Topological radicals, I. Basic properties, tensor products and joint quasinilpotence

Victor S. Shulman; Yuri V. Turovskii — 2005

Banach Center Publications

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