
Ukrainian mathematical congress  2009
Metin Basarir (Sakarya University, Turkey)
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
r^{q}(p,^{m}) = x = (x_{k}) Î w:^{m}x Î r^{q}(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.

