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Representation of p-Lattice Summing Operators

Abstract In this paper we study some aspects of the behaviour of p-lattice summing operators. We prove first that an operator T from a Banach space E to a Banach lattice X is p-lattice summing if and only if its bitranspose is. Using this theorem we prove a characterization for 1 -lattice summing operators defined on a C(K) space by means of the representing measure, which shows that in this case 1 -lattice and ∞-lattice summing operators coincide. We present also some results for the case 1 ≤ p < ∞ on C(K,E).