A Proof of the Invariant Subspace Conjecture for Separable Hilbert Spaces

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Charles W. Neville This is my paper · ORCID

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We prove the Invariant Subspace Conjecture for separable Hilbert spaces.

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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.