Compact operators on Riesz difference sequence space of fractional order

In this paper we study the domain of generalized Riesz difference matrix RqΔ(α) of fractional order α in the classical sequence spaces c0 and c and introduced the sequence spaces r0 q (Δ(α) ) and rc q (Δ(α) ). We obtain the α−, β− and γ−duals of these spaces and using Hausdorff measure of noncompactness, we characterize certain classes of compact operators on the space r0 q (Δ(α) ). Keywords: Riesz difference sequence space, Fractional Difference operator Δ(α) , α−, β− and γ−duals , Compact operator, Hausdorff measure of non-compactness.