Operators T that belong to some summing operator ideal, can be characterized by means of the continuity of an associated tensor operator T that is defined between tensor products of sequences spaces. In this paper we provide a unifying treatment of these tensor product characterizations of summing operators. We work in the more general frame provided by homogeneous polynomials, where an associated "tensor" polynomial-which plays the role of T-, needs to be determined first. Examples of applications are shown.
This paper introduces the class of Cohen p-nuclear m-linear operators between Banach spaces. A characterization in terms of Pietsch's domination theorem is proved. The interpretation in terms of factorization gives a factorization theorem similar to Kwapień's factorization theorem for dominated linear operators. Connections with the theory of absolutely summing m-linear operators are established. As a consequence of our results, we show that every Cohen p-nuclear (1 < p ≤ ∞) m-linear mapping on arbitrary Banach spaces is weakly compact.
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