Amenability, unitarizability, and strong Ulam stability
What the paper claims, in its own words
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.
The plain-language explainer for this entry is still coming.
The original papers (2)
- Unitarizability implies amenability for discrete groups (PDF, opens in a new tab) September 23, 2026 Formal proof listed
- Strong Ulam Stability Characterizes Amenability (PDF, opens in a new tab) October 5, 2026