On the Double Sequence Space H as an Extension of Hahn Space h
Abstract
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 H, where ∈\p,bp,r\, as an extension of the Hahn sequence space h. Our investigation begins with an analysis of several topological properties of H, apart from a comprehensive analysis of the relationship between Hahn double sequences and some other classical double sequence spaces. The α-dual, algebraic dual and β(bp)-dual, and γ-dual of the space H are detrmined. Furthermore, we define the determining set of H and we state the conditions concerning the characterization of four-dimensional (4D) matrix classes (H,λ), where λ=\H,BV, BV 0, CS,CS 0,BS\ and (μ,H), where μ=\Lu, C 0, C,Mu\. In conclusion, this research contributes non-standard investigation and various significant results into the space H. The conducted results are deepen the understanding of the space H and open up new avenues for further research and applications in sequence space theory.
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