In this paper, we introduce and study a new concept of summability in the category of multilinear operators, which is the Cohen strongly p-summing multilinear operators. We prove a natural analog of the Pietsch domination theorem and we compare the notion of p-dominated multilinear operators with this class by generalizing a theorem of Bu-Cohen.

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In the theory of p-summing operators studied by Pietsch we know that π 2 (C(K), H) = π p (C(K), H) for any Hilbert space H and any p such that 2 < p < +∞. In this paper we prove that this equality is not true in the same notion generalized by Junge and Pisier to operator spaces, i.e. π l 2 (B(l 2), OH) (= π 0 2 (B(l 2), OH)) = π l p (B(l 2), OH).

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