Topological radicals, III. Joint spectral radius
V. S. Shulman, Yu. V. Turovskii
TL;DR
This paper develops the theory of topological radicals, especially hypocompact radicals, and applies it to derive formulas for calculating the joint spectral radius of precompact families in Banach algebras.
Contribution
It introduces new theoretical tools in topological radicals and provides practical formulas for joint spectral radius computation in Banach algebras.
Findings
Formulas for joint spectral radius of precompact families
Development of hypocompact radical theory
Enhanced understanding of topological radicals
Abstract
We develop the theory of topological radicals, and in particular the theory of the hypocompact radical. The results are applied for obtaining convenient formulas of calculation of the joint spectral radius of a precompact family of elements in a Banach algebra.
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Taxonomy
TopicsAdvanced Operator Algebra Research · Spectral Theory in Mathematical Physics · Holomorphic and Operator Theory