Almost Sequence Spaces Derived by the Domain of the Matrix Ar

Abstract EN

By using Ar, we introduce the sequence spaces afr, af0r, and afsr of normed space and BK-space and prove that afr, af0r, and afsr are linearly isomorphic to the sequence spaces f, f0, and fs , respectively.

Further, we give some inclusion relations concerning the spaces afr, af0r, and the nonexistence of Schauder basis of the spaces fs and afsr is shown.

Finally, we determine the β- and γ-duals of the spaces afr and afsr.

Furthermore, the characterization of certain matrix classes on new almost convergent sequence and series spaces has exhaustively been examined.