Polynomial versions of almost Dunford-Pettis sets and almost limited sets in Banach lattices

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:485

Article

Shi, Zhongrui¹  Wang, Yu¹  Bu, Qingying² 

[1] Shanghai Univ, Dept Math, Shanghai 200444, Peoples R China

[2] Univ Mississippi, Dept Math, University, MS 38677 USA

关键词: Almost Dunford-Pettis set;    Almost limited set;    Regular homogeneous polynomial;    Fremlin tensor product;   

DOI  :  10.1016/j.jmaa.2019.123834

来源: Elsevier

【 摘 要 】

Let A be a norm bounded solid subset of a Banach lattice E and n be any positive integer. We prove that A is an almost Dunford-Pettis set if and only if every positive weakly compact n-homogeneous polynomial from E to c(0) maps A to a relatively compact set in c(0). Moreover, if E is sigma-Dedekind complete, we also prove that A is an almost limited set if and only if every positive n-homogeneous polynomial from E to co maps A to a relatively compact set in c(0). (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

Free