{"id":"openai-math/Invariant-projection-counterexamples-for-every-irrational-rotation","pdf":"https://github.com/openai/math/blob/main/preprints/Invariant-projection-counterexamples-for-every-irrational-rotation-September-27-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/Invariant-projection-counterexamples-for-every-irrational-rotation-September-27-2026","tags":["operator-algebras","ergodic-theory","von-neumann-algebras"],"score":0,"title":"Invariant-projection counterexamples for every irrational rotation","domain":"Operator algebras","family":"293","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.OA","summary":"For every irrational angle, we construct a continuous nonnegative circle weight with exactly one zero and logarithmic integral $`-\\infty`$ whose weighted rotation has no nontrivial invariant projection in the associated hyperfinite type II 1 factor. This answers negatively the question of Zhu, Fang, and Shi, with the angle prescribed in advance. The resulting operator is nonzero and norm-quasinilpotent.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-27","reactions":{},"formalized":false,"family_title":"Invariant projections, hyperinvariant subspaces, and transitive algebras"}