On some topological and geometric properties of generalized Riesz difference sequence space

In the present paper, we introduce the generalized Riesz difference sequence space r^q(p,^m) which is defined by

rq(p,m) = x = (xk) Î w:mx Î rq(p),

where r^q(p) is the Riesz sequence space defined by B. Altay and F. Basar. We give some topological properties, compute the duals and determine the Schauder basis of this space. Finally, we study the characterization of some matrix mappings on this sequence space. And the last section we investigate some geometric properties of r^q(p,^m) and we have proved that this sequence space has property () and the uniform Opial property for p_k ≥ 1.