Some Topological and Geometrical Properties of a New Difference Sequence Space

Abstract EN

We introduce the new difference sequence space apr(Δ) .

Further, it is proved that the space apr(Δ) is the BK-space including the space bvp, which is the space of sequences of pbounded variation.

We also show that the spaces apr(Δ), and ℓp are linearly isomorphic for 1≤p<∞.

Furthermore, the basis and the α-, β- and γ-duals of the space apr(Δ) are determined.

We devote the final section of the paper to examine some geometric properties of the space apr(Δ).