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The transitive algebra problem
Corollary 1.2 of the principal manuscript: the commutant of the constructed nonzero quasinilpotent operator is a proper, strongly closed, unital, transitive complex algebra, so it is not strongly dense in . This answers the question negatively on every infinite-dimensional separable Hilbert space. It is an immediate consequence of the hyperinvariant counterexample, since the commutant of an operator without hyperinvariant subspaces is transitive. The algebra is a commutant, so nothing is said about singly generated transitive algebras, which is the invariant subspace problem.
Exact FrontierDelta
Prior state unknown→disproved
Scope and record
Occurred: Sep 27, 2026
Delta type: SOURCE CLAIM
Assumptions: VibeMathed verification: lean-checked. Publication: announcement. AI contribution: ai-discovered. VibeMathed editorial classifications, scores, notes, relations, and dataset structure are CC BY 4.0. Source statements and linked content retain their own rights.
Canonical aliases: The transitive algebra problem · Transitive algebra problem
Confidence: Not scored
Registry verification: lean checked · announcement · candidate
Attribution
VibeMathed
registry · event recorded by
Unreleased internal OpenAI model
model · ai model contributor · OpenAI
Artifacts and verifiers
Compute record
No linked compute attempts recorded.
Lineage and corrections
Lean Comparator challenge BackwardIntertwiners (OpenAI math release) evidence for this event
VibeMathed record: The transitive algebra problem evidence for this event
This event attributed to Unreleased internal OpenAI model
Corollary 1.2 of the principal manuscript: the commutant of the constructed nonzero quasinilpotent operator is a proper, strongly closed, unital, transitive complex algebra, so it is not strongly dense in . This answers the question negatively on every infinite-dimensional separable Hilbert space. It is an immediate consequence of the hyperinvariant counterexample, since the commutant of an operator without hyperinvariant subspaces is transitive. The algebra is a commutant, so nothing is said about singly generated transitive algebras, which is the invariant subspace problem. parent of this event
The transitive algebra problem parent of this event
Backward intertwiners and a transitive commutant (companion) evidence for this event
Arveson 1967, A density theorem for operator algebras evidence for this event
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