Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4616413 | Journal of Mathematical Analysis and Applications | 2014 | 14 Pages |
Abstract
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 xâE has some local property if and only if its nonincreasing rearrangement xâ 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 Îp,Ï and Orlicz-Lorentz spaces ÎÏ,Ï (Sections 3, 4.1 and 4.2). We conclude with the description of global monotonicity structure of Lorentz spaces Îp,Ï (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).
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Maciej Ciesielski, PaweÅ Kolwicz, Agata Panfil,