C*-Algebras Isomorphically Representable On L(P)

Let p is an element of (1, infinity)\{2}. We show that every homomorphism from a C*-algebra A into B (l(p) (J)) satisfies a compactness property where J is any set. As a consequence, we show that a C*-algebra A is isomorphic to a subalgebra of B (l(p) (J)), for some set J, if and only if A is residually finite-dimensional.