Multiple summing operators on Banach spaces ✩

In this paper, we improve some previous results about multiple p-summing multilinear operators by showing that every multilinear form from L1 spaces is multiple p-summing for 1 p 2. The proof is based on the existence of a predual for the Banach space of multiple p-summing multilinear forms. We also show the failure of the inclusion theorem in this class of operators and improve some results of Y. Meléndez and A. Tonge about dominated multilinear operators.  2003 Elsevier Inc. All rights reserved