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math.FA2020
Pontryagin-Krein Theorem: Lomonosov's proof and related results
Edward Kissin, Victor S. Shulman, Yurii Turovskii
We discuss Lomonosov's proof of the Pontryagin-Krein Theorem on invariant maximal non-positive subspaces, prove the refinement of one theorem from \cite{OShT} on common fixed point…
math.FA2020
From Lomonosov Lemma to Radical Approach in Joint Spectral Radius Theory
Edward Kissin, Victor S. Shulman, Yurii Turovskii
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.…