On the space of p-summable difference sequences of order m, (1 <= p < infinity)
STUDIA SCIENTIARUM MATHEMATICARUM HUNGARICA, vol.43, no.4, pp.387-402, 2006 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 43 Issue: 4
- Publication Date: 2006
- Doi Number: 10.1556/sscmath.43.2006.4.1
- Journal Name: STUDIA SCIENTIARUM MATHEMATICARUM HUNGARICA
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Page Numbers: pp.387-402
- Inonu University Affiliated: No
Abstract
The difference sequence spaces l(infinity)(Delta), c(Delta) and c(0)(Delta) were studied by Kizmaz[8]. The difference sequence space bv(p), generated from the space l(p), has recently been introduced by Basar and Altay [5]. Several papers deal with the sets of sequences whose m(th) order difference are bounded, convergent or convergent to zero. The main purpose of the present paper is to introduce the space l(p)(Delta((m))) consisting of all sequences whole m(th) order differences are p-absolutely summable, and is to fill up the gap in the existing literature. Moreover, we give some topological properties and inclusion relations, a Schauder basis and determine the alpha-, beta-, gamma- and f-duals of the spaces l(p)(Delta((m))). The last section of the paper has been devoted to the characterization of the matrix mappings on the sequence space l(p)(Delta((m))).