John Bunce’s research while affiliated with University of Kansas and other places

In this paper it is proved that a C∗-algebra A is strongly amenable iff A satisfies a certain fixed point property when acting on a compact convex set, or iff a certain Hahn-Banach type extension theorem is true for all Banach A-modules. It is proved that a C∗-algebra A is amenable iff A satisfies a weaker Hahn-Banach type extension theorem.

B. E. Johnson has introduced the concept of a strongly amenable $C^\ast$-algebra and has proved that GCR algebras and uniformly hyperfinite algebras are strongly amenable. We generalize the well-known Dixmier-Mackey theorem on amenable groups by proving that every continuous representation of a strongly amenable $C^\ast$-algebra is similar to a $^\ast$-representation. As an application, we show that every invariant operator range for a Type I von Neumann algebra comes from an operator in the commutant.

B. E. Johnson has introduced the concept of a strongly amenable C*-algebra and has proved that GCR algebras and uniformly hyperfinite algebras are strongly amenable. We generalize the well-known Dixmier-Mackey theorem on amenable groups by proving that every continuous representation of a strongly amenable C*-algebra is similar to a ^representation. As an application, we show that every invariant operator range for a Type I von Neumann algebra comes from an operator in the commutant.