Pontryagin-Krein theorem: Lomonosov's proof and related results

Kissin, Edward, Shulman, Victor S. and Turovskii, Yuri V. (2020) Pontryagin-Krein theorem: Lomonosov's proof and related results. In: Advances in Analysis and Geometry, The Mathematical Legacy of Victor Lomonosov. Operator Theory. De Gruyter, Berlin, Boston, pp. 231-250. ISBN 978-3-11-065339-7

Abstract

We discuss Lomonosov's proof of the Pontryagin-Krein Theorem on invariant maximal non-positive subspaces, prove the refinement of one theorem from [22] on common fixed points for a group of fractional-linear maps of operator ball and deduce its consequences. Some Burnside-type counterparts of the Pontryagin-Krein Theorem are also considered.

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