On the invariant subspace problem in Hilbert spaces

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arxiv 2305.15442 v2 pith:4ULALJ25 submitted 2023-05-24 math.FA

Per H. Enflo This is my paper · ORCID

classification math.FA

keywords hilbertinvariantsubspaceboundedclosedeverylinearnon-trivial

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In this paper we show that every bounded linear operator T on a Hilbert space H has a closed non-trivial invariant subspace.

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Invariant submodules of modular operators and Lomonosov type theorem for Hilbert C*-modules
math.OA 2025-06 conditional novelty 5.0 of 10

A Lomonosov-type theorem holds for compact operators on non-finitely-generated Hilbert C*-modules over finite-dimensional C*-algebras: each such operator has a proper nonzero hyperinvariant submodule.