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arXiv · 1506.06311

Domination spaces and factorization of linear and multilinear summing operators

E. Dahia·D. Achour·P. Rueda·E. A. Sánchez Pérez
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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.

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E. Dahia, D. Achour, P. Rueda, E. A. Sánchez Pérez. 2015-06-21. Domination spaces and factorization of linear and multilinear summing operators. https://arxiv.org/abs/1506.06311

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