Almost absolute weighted summability with index k and matrix transformations

Abstract

Abstract In this paper we generalize the space ℓ ˆ k $\hat{\ell }_{k}$ of absolutely almost convergent series (J. Math. Anal. Appl. 161:50–56, 1991) via weighted mean transformations. We study some inclusion relations and their topological properties. Further we characterize certain matrix transformations.

Keywords

• Sequence spaces
• BK-spaces
• Absolute and almost summability
• Matrix transformations