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

Abstract EN

We introduce the spaces of A(λ)-null, A(λ)-convergent, and A(λ)-bounded sequences.

We examine some topological properties of the spaces and give some inclusion relations concerning these sequence spaces.

Furthermore, we compute α-, β-, and γ-duals of these spaces.

Finally, we characterize some classes of matrix transformations from the spaces of A(λ)-bounded and A(λ)-convergent sequences to the spaces of bounded, almost convergent, almost null, and convergent sequences and present a Steinhaus type theorem.