D. Achour | Searcharxiv

arXiv2024

Lattice sequence spaces and summing mappings

The objective of this study is to advance the theory concerning positive summing operators. Our focus lies in examining the space of positive strongly p-summable sequences and the space of positive unconditionally p-summable sequences. We utilize these in conjunction with the Banach lattice of positive weakly p-summable sequences to present and characterize the classes of positive strongly (p; q)-summing operators, positive (p; q)-summing, and positive Cohen (p; q)-nuclear operators. Additionally, we describe these classes in terms of the continuity of an associatedte nsor operator that is defined between tensor products of sequences spaces.

math.FA↗

arXiv2015

Domination spaces and factorization of linear and multilinear summing operators

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, $(p_1,\ldots,p_n)$-dominated multilinear operators and dominated $(p_1,\ldots, p_n;σ)$-continuous multilinear operators.

math.FA↗