c © 1997 Universitat de Barcelona On the positive absolutely summing operators on the space Lp (µ,X)

In this paper we obtain a characterization of the positive absolutely summing operators on the space Lp(µ, X) with 1 ≤ p < ∞ and X a Banach lattice, which is analogous with that given by Ch. Swartz in [8] for absolutely summing operators on the space of continuous vector valued functions. Throughout in this paper X will denote a Banach lattice, X+ = {x ∈ X | x ≥ 0} and B is a Banach space. Also, if Y is a normed space and y1,..., yn ∈ Y we write l1 yi | i = 1,