Amenable Banach algebra

Summary

An amenable Banach algebra is a Banach algebra for which every bounded derivation into every dual bimodule is inner. Barry Johnson introduced the notion. He proved that for a locally compact group $G$, the group algebra $L^1(G)$ is amenable exactly when $G$ is an amenable group. For C*-algebras, amenability is equivalent to being nuclear. It is one of the main finiteness conditions in the cohomology of Banach algebras.