Copyright © 2009 Metin Başarir and Mustafa Kayikçi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We introduce the generalized Riesz difference sequence space rq(p,Bm) which is defined by rq(p,Bm)={x=(xk)∈w:Bmx∈rq(p)} where rq(p) is the Riesz sequence space defined by Altay and Başar. We give some topological properties, compute the α_,β_ duals, and determine the Schauder basis of this space. Finally; we study the characterization of some matrix mappings on this sequence space. At the end of the paper, we investigate some geometric properties of rq(p,Bm) and we have proved that this sequence space has property (β) for pk≥1.