Geodesic
Geometric Properties and Compact Operator on Fractional Riesz Difference Space
Kragujevac Journal of Mathematics, Tome 47 (2023) no. 4, p. 545
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In this article we introduce the Riesz difference sequence space $r_p^q\left(\Delta^{B\alpha}\right)$ of fractional order $\alpha,$ defined by the composition of fractional backward difference operator $\Delta^{B\alpha}$ given by $(\Delta^{B\alpha}v)_k=\sum_{i=0}^{\infty}(-1)^i\frac{\Gamma(\alpha+1)}{i!\Gamma(\alpha-i+1)}v_{k-i}$ and the Riesz matrix $R^q.$ 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 $r_p^q\left(\Delta^{B\alpha}\right)$. Finally, we characterize certain classes of compact operators on the space $r_p^q\left(\Delta^{B\alpha}\right)$ using Hausdorff measure of non-compactness.
Classification : 46A45 46A35, 46B45, 47B07
Keywords: Riesz difference sequence space, difference operator $\Delta^B\alpha;$ geometric properties, Hausdorff measure of non-compactness 
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     author = {Taja Yaying and Bipan Hazarika and Ayhan Esi},
     title = {Geometric {Properties} and {Compact} {Operator} on {Fractional} {Riesz} {Difference} {Space}},
     journal = {Kragujevac Journal of Mathematics},
     pages = {545 },
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     number = {4},
     language = {en},
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Taja Yaying; Bipan Hazarika; Ayhan Esi. Geometric Properties and Compact Operator on Fractional Riesz Difference Space. Kragujevac Journal of Mathematics, Tome 47 (2023) no. 4, p. 545 . http://geodesic.mathdoc.fr/item/KJM_2023_47_4_a5/