On the difference spaces of almost convergent and strongly almost convergent double sequences

Abstract

In this paper, we study the difference spaces $${\mathcal {F}}(\varDelta )$$, $${\mathcal {F}}_0(\varDelta )$$, $${\mathcal {[F]}}(\varDelta )$$ and $${\mathcal {[F]}}_0(\varDelta )$$ of double sequences obtained as the domain of four-dimensional backward difference matrix $$\varDelta $$ in the spaces $${\mathcal {F}}$$, $${\mathcal {F}}_{0}$$, $${\mathcal {[F]}}$$ and $${\mathcal {[F]}}_{0}$$ of almost convergent, almost null, strongly almost convergent and strongly almost null double sequences; respectively. We examine general topological properties of those spaces and give some inclusion theorems. Furthermore, we deal with their dual spaces.