On some geometric and topological properties of generalized Orlicz–Lorentz sequence spaces |
| |
| Authors: | Paweł Foralewski Henryk Hudzik Lucjan Szymaszkiewicz |
| |
| Institution: | 1. Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Umultowska 87, 61‐614 Poznań, Poland;2. Phone: +48 61 8295377, Fax: +48 61 8295315;3. Institute of Mathematics, Szczecin University, Wielkopolska 15, 70‐451 Szczecin, Poland;4. Phone: +48 91 4441219, Fax: +48 91 4441226 |
| |
| Abstract: | Generalized Orlicz–Lorentz sequence spaces λφ generated by Musielak‐Orlicz functions φ satisfying some growth and regularity conditions (see 28] and 33]) are investigated. A regularity condition δλ 2 for φ is defined in such a way that it guarantees many positive topological and geometric properties of λφ. The problems of the Fatou property, the order continuity and the Kadec–Klee property with respect to the uniform convergence of the space λφ are considered. Moreover, some embeddings between λφ 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 λφ, 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) |
| |
| Keywords: | Generalized Orlicz− Lorentz sequence space Orlicz− Lorentz sequence space Fatou property order continuity embeddings strict monotonicity lower local uniform monotonicity upper local uniform monotonicity rotundity |
|
|
