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

2024/06/07 by Orhan Tuǧ, Tuǧ, Orhan, Eberhard Malkowsky +5
Mathematics · #40C05 #46A45 #Advanced Banach Space Theory #Approximation Theory and Sequence Spaces #FOS: Mathematics #Fixed Point Theorems Analysis #Functional Analysis (math.FA)

paper · pdf · doi:10.48550/arxiv.2406.05117

openalex publication_date 2024/06/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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_ϑ, 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 H_ϑ, 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_ϑ are detrmined. Furthermore, we define the determining set of H_ϑ and we state the conditions concerning the characterization of four-dimensional (4D) matrix classes (H_ϑ,λ), where λ=\H_ϑ,BV, BV_{ϑ 0}, CS_ϑ,CS_{ϑ 0},BS\ and (μ,H_ϑ), where μ=\L_u, C_{ϑ 0}, C_ϑ,M_u\. In conclusion, this research contributes non-standard investigation and various significant results into the space H_ϑ. The conducted results are deepen the understanding of the space H_ϑ and open up new avenues for further research and applications in sequence space theory.

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