{"id":"openai-math/Expected-amenable-subalgebras-preserving-core-commutants","pdf":"https://github.com/openai/math/blob/main/preprints/Expected-amenable-subalgebras-preserving-core-commutants-September-23-2026/Expected-amenable-subalgebras-preserving-core-commutants-September-23-2026.pdf","url":"https://github.com/openai/math/tree/main/preprints/Expected-amenable-subalgebras-preserving-core-commutants-September-23-2026","tags":["von-neumann-algebras","operator-algebras","conditional-expectation"],"score":0,"title":"Expected amenable subalgebras preserving core commutants","domain":"Operator algebras","family":"290","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.OA","summary":"We prove that every inclusion $`N\\subset M`$ of von Neumann algebras with separable preduals and a faithful normal conditional expectation contains an expected amenable subalgebra $`P\\subset N`$ such that $`P'\\cap c(M)=N'\\cap c(M)`$, where $`c(M)`$ denotes the continuous core of M . This resolves the relative bicentralizer conjecture in this setting.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-23","reactions":{},"formalized":false,"family_title":"Relative bicentralizers and modular spectral recovery"}