On the Domain of the Triangle A ( λ ) on the Spaces of Null, Convergent, and Bounded Sequences

Abstract

We introduce the spaces of $A(\lambda )$-null, $A(\lambda )$-convergent, and $A(\lambda )$-bounded sequences. We examine some topological properties of the spaces and give some inclusion relations concerning these sequence spaces. Furthermore, we compute $\alpha$-, $\beta$-, and $\gamma$-duals of these spaces. Finally, we characterize some classes of matrix transformations from the spaces of $A(\lambda )$-bounded and $A(\lambda )$-convergent sequences to the spaces of bounded, almost convergent, almost null, and convergent sequences and present a Steinhaus type theorem.