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Unitarizability implies amenability for discrete groups

OpenAI

OpenAI Mathopenai-math/Unitarizability-Implies-Amenability-for-Countable-GroupsSep 23, 2026math.GRAI-generatedscore 0

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.

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