{"id":"openai-math/Approximation-Paving-over-Arbitrary-Maximal-Abelian-Subalgebras","pdf":"https://github.com/openai/math/blob/main/preprints/Approximation-Paving-over-Arbitrary-Maximal-Abelian-Subalgebras-September-25-2026/Approximation-Paving-over-Arbitrary-Maximal-Abelian-Subalgebras-September-25-2026.pdf","url":"https://github.com/openai/math/tree/main/preprints/Approximation-Paving-over-Arbitrary-Maximal-Abelian-Subalgebras-September-25-2026","tags":["operator-algebras","von-neumann-algebras","approximation-paving"],"score":0,"title":"Approximation Paving over Arbitrary Maximal Abelian Subalgebras","domain":"Operator algebras","family":"300","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.OA","summary":"We prove the approximation-paving conjecture of Popa and Vaes for every maximal abelian subalgebra of a complex von Neumann algebra. For each $`0\\lt \\varepsilon\\lt 1`$, every self-adjoint operator is a strong limit of self-adjoint operators of norm at most three times its norm, each admitting a norm paving with error at most ε times the approximant's own norm. The number of projections is at most $`C\\varepsilon^{-6}`$ for a universal constant C . No separability or conditional-expectation hypothesis is required.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-25","reactions":{},"formalized":false,"family_title":"Approximation and quadratic strong-operator paving"}