{"id":"openai-math/Backward-intertwiners-and-a-transitive-commutant","pdf":"https://github.com/openai/math/blob/main/preprints/Backward-intertwiners-and-a-transitive-commutant-September-27-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/Backward-intertwiners-and-a-transitive-commutant-September-27-2026","tags":["operator-theory","invariant-subspaces","hilbert-space"],"score":0,"title":"Backward intertwiners and a transitive commutant","domain":"Operator algebras","family":"293","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.OA","summary":"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.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-27","reactions":{},"formalized":true,"family_title":"Invariant projections, hyperinvariant subspaces, and transitive algebras"}