Local monotonicity structure of symmetric spaces with applications

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:409

Article

Ciesielski, Maciej¹  Kolwicz, Pawel¹  Panfil, Agata² 

[1] Poznan Univ Tech, Inst Math, PL-60965 Poznan, Poland

[2] Adam Mickiewicz Univ, Fac Math & Comp Sci, PL-61614 Poznan, Poland

关键词: Symmetric Banach function spaces;    Orlicz-Lorentz spaces;    Lorentz spaces of maximal functions;    Best dominated approximation problems;    Local (global) monotonicity structure;    Order continuity;   

DOI  :  10.1016/j.jmaa.2013.07.028

来源: Elsevier

【 摘 要 】

In this paper we discuss several monotonicity properties in Banach lattices. We start with several general results on local structure of symmetric Banach function spaces discussing in particular whether a point x is an element of E has some local property if and only if its nonincreasing rearrangement x* has the same property (Section 2). In that section we also prove some general facts for nonincreasing rearrangements which may be of independent interest. Next, we apply these results to find complete criteria for local monotonicity structure of Lorentz spaces Gamma(p.omega) and Orlicz-Lorentz spaces Lambda(phi,omega) (Sections 3, 4.1 and 4.2). We conclude with the description of global monotonicity structure of Lorentz spaces Gamma(p.omega) (Section 4.3). We finish with the applications of upper monotonicity and lower monotonicity points to local best dominated approximation problems in Banach lattices (Section 5). (c) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

Free