Abstract of a paper by E. Dahia, D. Achour, P. Rueda and E. A. Sanchez Perez
This is an announcement for the paper "Domination spaces and factorization of linear and multilinear summing operators" by E. Dahia, D. Achour, P. Rueda and E. A. Sanchez Perez. Abstract: 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. Archive classification: math.FA Submitted from: hajdahia@univ-msila.dz The paper may be downloaded from the archive by web browser from URL http://front.math.ucdavis.edu/1506.06311 or http://arXiv.org/abs/1506.06311
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