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In this paper we discuss the infinite-dimensional generalizations of thefamous theorem of Berger-Wang (generalized Berger-Wang formulas) and give anoperator-theoretic proof of I. Morris's theorem about coincidence of threeessential joint spectral radius, related to these formulas. Further we developBanach-algebraic approach based on the theory of topological radicals, andobtain some new results about these radicals.

From Lomonosov Lemma to Radical Approach in Joint Spectral Radius Theory