Linear isomorphic spaces of fractional-order difference operators

Abstract

In the present paper, we intend to make an approach to introduce and study the applications of fractional-order difference operators by generating Orlicz almost null and almost convergent sequence spaces. We also show that aforesaid spaces are linearly isomorphic and BK-spaces. Further, we investigate inclusion relations between newly formed sequence spaces and compute the β-, γ-duals. Moreover, we characterize several classes of infinite matrices and give some interesting examples. Finally, we study aforesaid sequence spaces over n-normed space and demonstrate their several algebraic and topological properties.

Keywords

• 47A15
• 46A35
• 46A45
• 40A05