UNCONDITIONALLY CONVERGING AND COMPACT-OPERATORS ON CO

It is shown that if Y is a Banach space, then c0 imbeds in Y if and only if for every infinite dimensional Banach space X, there exists a noncompact operator T : X --> Y. In order to prove this, we first examine properties of operators on c0, showing that if T : c0 --> X is a noncompact operator, then there exists a subspace Z of c0 such that Z is isomorphic to c0 and T\z is an isomorphism.