2015/06/21 by Elhadj Dahia, Dahmane Achour, Dahia, E. +5
Mathematics · #Advanced Banach Space Theory #Approximation Theory and Sequence Spaces #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory
paper · pdf · doi:10.48550/arxiv.1506.06311
openalex publication_date 2015/06/21 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
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.