Geodesic
Geometric Properties and Compact Operator on Fractional Riesz Difference Space
Kragujevac Journal of Mathematics, Tome 47 (2023) no. 4, p. 545 .

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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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     title = {Geometric {Properties} and {Compact} {Operator} on {Fractional} {Riesz} {Difference} {Space}},
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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/