Operators with an integral representation

We introduce a fairly large class of bounded linear operators between Banach spaces which admit an integral representation. It turns out that an operator belongs to this class if and only if it factors through a C(K) space. As an application, we characterize Banach spaces containing no copy of c0,Banach spaces containing no complemented copy of ℓ1, Grothendieck spaces, and L∞-spaces. We also study C(K)-factorization and extension properties of absolutely continuous operators, giving a partial answer to a question raised in 1985 by H. Jarchow and U. Matter