On Some Generalized <inline-formula> <graphic file="1029-242X-2011-485730-i1.gif"/></inline-formula>-Difference Riesz Sequence Spaces and Uniform Opial Property

Abstract

Abstract We define the new generalized difference Riesz sequence spaces , , and which consist of all the sequences whose -transforms are in the Riesz sequence spaces , , and , respectively, introduced by Altay and Başar (2006). We examine some topological properties and compute the -, -, and -duals of the spaces , , and . Finally, we determine the necessary and sufficient conditions on the matrix transformation from the spaces , , and to the spaces and and prove that sequence spaces and have the uniform Opial property for for all .