Algebra · Oct 6, 2026
Amenability, unitarizability, and strong Ulam stability
Resolves Dixmier's problem for all discrete groups: amenability is equivalent to every uniformly bounded Hilbert-space representation being similar to a unitary representation. For countable discrete groups, amenability is also equivalent to strong Ulam stability: sufficiently accurate unitary approximate representations are uniformly close in operator norm to genuine representations on the same, possibly infinite-dimensional, Hilbert space.
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