15. From Lomonosov lemma to radical approach in joint spectral radius theory

Abstract

In this paper we discuss the infinite-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.