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