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From Lomonosov Lemma to radical approach in joint spectral radius theory

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Kissin, Edward, Shulman, Victor S. and Turovskii, Yuri V. (2019) From Lomonosov Lemma to radical approach in joint spectral radius theory. In: Advances in Analysis and Geometry, The Mathematical Legacy of Victor Lomonosov. Operator Theory,. De Gruyter, Berlin, Boston, pp. 205-230. ISBN 978-3-11-065339-7

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Abstract

In this paper we discuss the infnite-dimensional generalizations of the famous theorem of Berger-Wang (generalized Berger-Wang formulas) and give an operator-theoretic proof of I. Morris's theorem about coincidence of three essential joint spectral radius, related to these formulas. Further we develop Banach-algebraic approach based on the theory of topological radicals, and obtain some new results about these radicals.

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