On the Double Sequence Space Hϑ as an Extension of Hahn Space <i>h</i>

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 , where ϑ ∈ { p , b p , r }, as an extension of the Hahn sequence space h . Our investigation begins with an analysis of several topological properties of , apart from a comprehensive analysis of the relationship between Hahn double sequences and other classical double sequence spaces. The α − dual, algebraic dual and β ( b p )− dual, and γ − dual of the space are determined. Furthermore, we define the determining set of and we state the conditions concerning the characterization of four‐dimensional (4D) matrix classes , where and , where . In conclusion, this research contributes to nonstandard investigation and various significant results in the space . The conducted results deepen the understanding of space and open up new avenues for further research and applications in sequence space theory.