%0 Journal Article
%T Domination spaces and factorization of linear and multilinear summing operators
%A E. Dahia
%A D. Achour
%A P. Rueda
%A E. A. S¨˘nchez P¨Śrez
%J Mathematics
%D 2015
%I arXiv
%X 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, $(p,\sigma)$-absolutely continuous linear operators, factorable strongly $p$-summing multilinear operators, $(p_1,\ldots,p_n)$-dominated multilinear operators and dominated $(p_1,\ldots, p_n;\sigma)$-continuous multilinear operators.
%U http://arxiv.org/abs/1506.06311v2