GEOMETRIC PROPERTIES AND COMPACT OPERATOR ON FRACTIONAL RIESZ DIFFERENCE SPACE

In this article we introduce the Riesz difference sequence space r(p)(q)(Delta(B alpha)) of fractional order a, defined by the composition of fractional backward difference operator Delta(B alpha) given by (Delta(B alpha)upsilon)(k) = Sigma(8)(i=0)(-1)(i)/Gamma(alpha+1) /iota!Gamma(alpha-i+1) upsilon(k- i) and the Riesz matrix Rq. We give some topological properties, obtain the Schauder basis and determine the alpha-, beta- and gamma- duals and investigate certain geometric properties of the space r(p)(q)(Delta(B alpha)). Finally, we characterize certain classes of compact operators on the space r(p)(q)(Delta(B alpha)) using Hausdorff measure of non-compactness.