Geometric Properties and Compact Operator on Fractional Riesz Difference Space
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Authors: T. YAYING, B. HAZARIKA AND A. ESI
DOI: 10.46793/KgJMat2304.545Y
Abstract:
In this article we introduce the Riesz difference sequence space rpq of fractional order α, defined by the composition of fractional backward difference operator ΔBα given by (ΔBαv)k = ∑ i=0∞(−1)ivk−i and the Riesz matrix Rq. We give some topological properties, obtain the Schauder basis and determine the α-, β- and γ- duals and investigate certain geometric properties of the space rpq. Finally, we characterize certain classes of compact operators on the space rpq using Hausdorff measure of non-compactness.
Keywords:
Riesz difference sequence space, difference operator ΔBα, geometric properties, Hausdorff measure of non-compactness.
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