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Backward intertwiners and a transitive commutant

OpenAI

OpenAI Mathopenai-math/Backward-intertwiners-and-a-transitive-commutantSep 27, 2026math.OAAI-generatedscore 0

We give a negative answer to the hyperinvariant-subspace problem by constructing, on every infinite-dimensional separable complex Hilbert space, a nonzero bounded norm-quasinilpotent operator with no nonzero proper closed hyperinvariant subspace. Its commutant is a proper strongly closed unital transitive complex operator algebra.

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