Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4673095 | Indagationes Mathematicae | 2013 | 27 Pages |
Abstract
In this paper, we continue investigations concerning generalized Orlicz-Lorentz sequence spaces Î»Ï initiated in the papers of Foralewski et al. (2008) [16,17] (cf. also Foralewski (2011) [11,12]). As we will show in Examples 1.1-1.3 the class of generalized Orlicz-Lorentz sequence spaces is much more wider than the class of classical Orlicz-Lorentz sequence spaces. Moreover, it is shown that if a Musielak-Orlicz function Ï satisfies condition δ2λ, then Î»Ï has the coordinatewise Kadec-Klee property. Next, monotonicity properties are considered. In order to get sufficient conditions for uniform monotonicity of the space λÏ, a strong condition of δ2 type and the notion of regularity of function Ï are introduced. Finally, criteria for non-squareness of λÏ, of their subspaces of order continuous elements (λÏ)a as well as of finite dimensional subspaces λÏn of Î»Ï are presented.
Related Topics
Physical Sciences and Engineering
Mathematics
Mathematics (General)
Authors
PaweÅ Foralewski,