Abstract
We apply the geometric approach provided by Σ-operators to develop a theory of p-summability for multilinear operators. In this way, we introduce the notion of Lipschitz p-summing multilinear operators and show that it is consistent with a general panorama of generalization: Namely, they satisfy Pietsch-type domination and factorization theorems and generalizations of the inclusion Theorem, Grothendieck's coincidence Theorems, the weak Dvoretsky-Rogers Theorem and a Lindenstrauss-Pełczyńsky Theorem. We also characterize this new class in tensorial terms by means of a Chevet-Saphar-type tensor norm. Moreover, we introduce the notion of Dunford-Pettis multilinear operators. With them, we characterize when a projective tensor product contains ℓ1. Relations between Lipschitz p-summing multilinear operators with Dunford-Pettis and Hilbert-Schmidt multilinear operators are given.
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