A C-algebra A is deened to be purely innnite if there are no characters on A, and if for every pair of positive elements a; b in A, such that b lies in the closed two-sided ideal generated by a, there exists a sequence fr n g in A such that r n ar n ! b. This deenition agrees with the usual deenition by J. Cuntz when A is simple. It is shown that the property of being purely innnite is preserve...

Let (Ω,Σ, μ) be a purely non-atomic measure space, and let 1 < p < ∞. If L(Ω,Σ, μ) is isomorphic, as a Banach space, to L(Ω,Σ, μ) for some purely atomic measure space (Ω,Σ, μ), then there is a measurable partition Ω = Ω1 ∪Ω2 such that (Ω1,Σ ∩ Ω1, μ|Σ∩Ω1) is countably generated and σ-finite, and that μ(σ) = 0 or ∞ for every measurable σ ⊆ Ω2. In particular, L(Ω,Σ, μ) is isomorphic to l.

In this paper, we illustrate certain criteria which are sufficient for a henselian valued field to admit non-isomorphic maximal purely wild extensions.

In this paper we show that if A is a unital Banach algebra and B is a purely innite C*-algebra such that has a non-zero commutative maximal ideal and $phi:A rightarrow B$ is a unital surjective spectrum preserving linear map. Then $phi$ is a Jordan homomorphism.