Absolutely continuous multilinear operators

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:397

Article

Dahia, E.²  Achour, D.²  Sanchez Perez, E. A.¹ 

[1] Univ Politecn Valencia, Inst Univ Matermat Pura & Aplicada, Valencia 46022, Spain

[2] Univ Msila, Lab Anal Fonct & Geometrie Espaces, Msila 28000, Algeria

关键词: Absolutely continuous operator;    Multilinear operator;    Pietsch domination theorem;    Tensor norm;    Banach function space;    Compact operator;   

DOI  :  10.1016/j.jmaa.2012.07.034

来源: Elsevier

【 摘 要 】

We introduce the new class of the (p; p(1), ... , p(m); sigma)-absolutely continuous multilinear operators, that is defined using a summability property that provides the multilinear version of the (p, sigma)-absolutely continuous operators. We give an analogue of the Pietsch domination theorem and a multilinear version of the associated factorization theorem that holds for (p, sigma)-absolutely continuous operators, obtaining in this way a rich factorization theory. We present also a tensor norm which represents this multi-ideal by trace duality. As an application, we show that (p; p(1), ... , p(m); sigma)-absolutely continuous multilinear operators are compact under some requirements. Applications to factorization of linear maps on Banach function spaces through interpolation spaces are also given. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free