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Domination spaces and factorization of linear and multilinear summing operators

2015

[EN] It is well known that not every summability property for multilinear 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. 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), ... , p(n))-dominated multilinear operators and dominated (p(1), ... , p(n); sigma)-continuous multilinear operators.

Discrete mathematicsMultilinear mapPietsch's domination theoremMultilinear summing operators010102 general mathematicsMathematics::Classical Analysis and ODEs010103 numerical & computational mathematicsPietsch's domination theorem factorization of operators multilinear summing operators.Factorization of operators01 natural sciencesFunctional Analysis (math.FA)Mathematics - Functional AnalysisMathematics (miscellaneous)FactorizationFOS: Mathematics0101 mathematicsMATEMATICA APLICADAMathematics
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