On some geometric and topological properties of generalized Orlicz–Lorentz sequence spaces

✍ Scribed by Paweł Foralewski; Henryk Hudzik; Lucjan Szymaszkiewicz

• Publisher: John Wiley and Sons
• Year: 2008
• Tongue: English
• Weight: 257 KB
• Volume: 281
• Category: Article
• ISSN: 0025-584X
• DOI: 10.1002/mana.200510594

✦ Synopsis

Abstract

Generalized Orlicz–Lorentz sequence spaces λ~φ~ generated by Musielak‐Orlicz functions φ satisfying some growth and regularity conditions (see [28] and [33]) are investigated. A regularity condition δ^λ^ ~2~ for φ is defined in such a way that it guarantees many positive topological and geometric properties of λ~φ~. The problems of the Fatou property, the order continuity and the Kadec–Klee property with respect to the uniform convergence of the space λ~φ~ are considered. Moreover, some embeddings between λ~φ~ and their two subspaces are established and strict monotonicity as well as lower and upper local uniform monotonicities are characterized. Finally, necessary and sufficient conditions for rotundity of λ~φ~, their subspaces of order continuous elements and finite dimensional subspaces are presented. This paper generalizes the results from [19], [4] and [17]. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)