0000000000328821
AUTHOR
Enrique Alfonso Sánchez Pérez
Representation and factorization theorems for almost-Lp-spaces
The first and fourth authors gratefully acknowledge the support of Ministerio de Ciencia, Innovacibn y Universidades (Spain), Agencia Estatal de Investigaciones, and FEDER, under projects MTM2014-53009-P (J.M. Calabuig) and MTM2016-77054-C2-1-P (E.A. Sanchez Perez).
The support localization property of the strongly embedded subspaces of banach function spaces
[EN] Motivated by the well known Kadec-Pelczynski disjointifcation theorem, we undertake an analysis of the supports of non-zero functions in strongly embedded subspaces of Banach functions spaces. The main aim is to isolate those properties that bring additional information on strongly embedded subspaces. This is the case of the support localization property, which is a necessary condition fulflled by all strongly embedded subspaces. Several examples that involve Rademacher functions, the Volterra operator, Lorentz spaces or Orlicz spaces are provided.
Domination spaces and factorization of linear and multilinear summing operators
[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.