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.
In this paper we introduce and study a new class containing the class of absolutely summing multilinear mappings, which we call absolutely (p; q 1 , . . . , q m ; r)-summing multilinear mappings. We investigate some interesting properties concerning the absolutely (p; q 1 , . . . , q m ; r)-summing m-linear mappings defined on Banach spaces. In particular, we prove a kind of Pietsch's Domination Theorem and a multilinear version of the Factorization Theorem.
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.
Abstract. We introduce the new class of the absolutely (p; p1, ..., pm; σ)-continuous multilinear operators, that is defined using a summability property that provides the multilinear version of the absolutely (p, σ)-continuous operators. We give an analogue of Pietsch's Domination Theorem and a multilinear version of the associated Factorization Theorem that holds for absolutely (p, σ)-continuous operators, obtaining in this way a rich factorization theory. We present also a tensor norm which represents this multiideal by trace duality. As an application, we show that absolutely (p; p1, ..., pm; σ)-continuous multilinear operators are compact under some requirements. Applications to factorization of linear maps on Banach function spaces through interpolation spaces are also given.
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