Domination spaces and factorization of linear and multilinear summing operators

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It is well known that not every summability property for non linear operators leads to a factorization theorem. In this paper we undertake a detailed study of factorization schemes for summing linear and nonlinear operators. Our aim is to integrate under the same theory a wide family of classes of mappings for which a Pietsch type factorization theorem holds. We analyze the class of linear operators that are defined by a summability inequality involving a homogeneous map. Our construction includes the cases of absolutely p-summing linear operators, (p,σ)-absolutely continuous linear operators, factorable strongly p-summing multilinear operators, (p₁,,pₙ)-dominated multilinear operators and dominated (p₁,, pₙ;σ)-continuous multilinear operators.