{"id":"openai-math/Unitarizability-Implies-Amenability-for-Countable-Groups","pdf":"https://github.com/openai/math/blob/main/preprints/Unitarizability-Implies-Amenability-for-Countable-Groups-September-23-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/Unitarizability-Implies-Amenability-for-Countable-Groups-September-23-2026","tags":["operator-algebras","amenability","group-representations","functional-analysis"],"score":0,"title":"Unitarizability implies amenability for discrete groups","domain":"Group theory","family":"251","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.GR","summary":"We prove that a discrete group is amenable if and only if every uniformly bounded representation on a complex Hilbert space is similar to a unitary representation. This resolves Dixmier's unitarizability problem affirmatively for discrete groups.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-23","reactions":{},"formalized":true,"family_title":"Amenability, unitarizability, and strong Ulam stability"}