Four-dimensional generalized difference matrix and some double sequence spaces

In this study, I introduce some new double sequence spaces B(Mu), B(Cp), B(Cbp), B(Cr) and B(Lq) as the domain of four-dimensional generalized difference matrix B(r,s,t,u) in the spaces Mu, Cp, Cbp, Cr and Lq, respectively. I show that the double sequence spaces B(Mu), B(Cbp) and B(Cr) are the Banach spaces under some certain conditions. I give some inclusion relations with some topological properties. Moreover, I determine the α-dual of the spaces B(Mu) and B(Cbp), the β(ϑ)-duals of the spaces B(Mu), B(Cp), B(Cbp), B(Cr) and B(Lq), where ϑ∈{p,bp,r}, and the γ-dual of the spaces B(Mu), B(Cbp) and B(Lq). Finally, I characterize the classes of four-dimensional matrix mappings defined on the spaces B(Mu), B(Cp), B(Cbp), B(Cr) and B(Lq) of double sequences

Some topological properties of the spaces of almost null and almost convergent double sequences

Let Cf0 and Cf denote the spaces of almost null and almost convergent double sequences, respectively. We show that Cf0 and Cf are BDK-spaces, barreled and bornological, but they are not monotone and so not solid. Additionally, we establish that both of the spaces Cf0 and Cf include the space BS of bounded double series. © TÜBITAK

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

In this paper, we study the difference spaces F(), F0(), [F]() and [F]0() of double sequences obtained as the domain of four-dimensional backward difference matrix in the spaces F, F0, [F] and [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