The Dixmier unitarizability problem asks whether every unitarizable group is an amenable group. The group is discrete, and the representations act on arbitrary complex Hilbert spaces. Amenability implies unitarizability, so the question concerns the reverse implication.
Dixmier Unitarizability Problem
See also
Amenable Group, Group Representation, Hilbert Space, Uniformly Bounded Representation, Unitarizable Group, Unitary RepresentationExplore with Wolfram|Alpha
References
Pisier, G. "Are Unitarizable Groups Amenable?" In Infinite Groups: Geometric, Combinatorial and Dynamical Aspects (Ed. L. Bartholdi, T. Ceccherini-Silberstein, T. Smirnova-Nagnibeda, and A. Zuk). Basel, Switzerland: Birkhäuser, pp. 323-362, 2005. https://doi.org/10.1007/3-7643-7447-0_8.Cite this as:
Weisstein, Eric W. "Dixmier Unitarizability Problem." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/DixmierUnitarizabilityProblem.html