ON THE RELATION BETWEEN ABSOLUTELY SUMMING OPERATORS AND NUCLEAR OPERATORS

Abstract

 It is known that every absolutely summing operator acting between C(W), where W is an arbitrary compact set, and a space, F, with the Radon-Nikodym property is nuclear. The purpose of this paper is to show that composing a weakly compact operator with an absolutely summing one we obtain a nuclear operator even the space, F, has not the Radon-Nikodym property. We give, also, a proof for the "factorisation" theorem and we put an interesting problem.