On the Double Sequence Space Hϑ as an Extension of Hahn Space h

Double sequence spaces have become a significant area of research within functional analysis due to their applications in various branches of mathematics and mathematical physics. In this study, we investigate Hahn double sequence space denoted as Hϑ, where ϑ∈p,bp,r, as an extension of the Hahn sequence space h. Our investigation begins with an analysis of several topological properties of Hϑ, apart from a comprehensive analysis of the relationship between Hahn double sequences and other classical double sequence spaces. The α− dual, algebraic dual and βbp− dual, and γ− dual of the space Hϑ are determined. Furthermore, we define the determining set of Hϑ and we state the conditions concerning the characterization of four-dimensional (4D) matrix classes Hϑ,λ, where λ=Hϑ,BV,BVϑ0,CSϑ,CSϑ0,BS and μ,Hϑ, where μ=Lu,Cϑ0,Cϑ,Mu. In conclusion, this research contributes to nonstandard investigation and various significant results in the space Hϑ. The conducted results deepen the understanding of space Hϑ and open up new avenues for further research and applications in sequence space theory.