On the Generalized Bm-Riesz Difference Sequence Space and β-Property

We introduce the generalized Riesz difference sequence space r(q)(p, B-m) which is defined by r(q)(p, B-m) = {x = (x(k)) is an element of w : B(m)x is an element of r(q)(p)} where r(q)(p) is the Riesz sequence space defined by Altay and Basar. We give some topological properties, compute the alpha_, beta_ 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 r(q)(p, B-m) and we have proved that this sequence space has property (beta) for p(k) >= 1. Copyright (C) 2009 M. Basarir and M. Kayikci.