Purely infinite C*-algebras from boundary actions of discrete groups.
Let (Ω,∑,μ) be a purely non-atomic measure space, and let 1 < p < ∞. If is isomorphic, as a Banach space, to for some purely atomic measure space (Ω’,∑’,μ’), then there is a measurable partition such that is countably generated and σ-finite, and that μ(σ) = 0 or ∞ for every measurable . In particular, is isomorphic to .