What does this research mean for the field?

The paranormed sequence space generated by a triangle over Maddox's space ℓ(q) involving the arithmetic divisor sum function possesses distinct algebraic, topological, and geometric properties, with fully characterizable Schauder bases, duals, and matrix classes. Novelty: ClaimNovelty.INCREMENTAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

To investigate the algebraic and topological properties of paranormed sequence spaces generated by a triangle and bounded sequences.

April 15, 2026Open Access

Some Paranormed Sequence Spaces Which Involve Arithmetic Divisor Sum Function

Key Points

To investigate the algebraic and topological properties of paranormed sequence spaces generated by a triangle and bounded sequences.
Study the properties of paranormed sequence spaces over Maddox's space ℓ(q).
Identify the Schauder basis and the α, β, and γ duals of these spaces.
Characterize various matrix classes related to ℓ∞, c, and c0.
The paper identifies the complete structure of the Schauder basis for the paranormed sequence space.
Characterization of multiple matrix classes provides new insights into the connections between them.
Geometric properties of the space are revealed, enhancing the understanding of its topology.

Abstract

Let , r ≥ 0, be a triangle and q = ( q j ) be a bounded sequence of strictly positive numbers. In this paper, we study the algebraic and topological properties of the paranormed sequence space , generated by the triangle over Maddox′s space ℓ ( q ). We identify the Schauder basis as well as the α ‐, β ‐, and γ ‐duals of the space . One section is devoted to characterizing matrix classes , where is any of the spaces ℓ ∞ , c , and c 0 , and also presents the characterization of some other matrix classes related to the space as corollaries derived from a main result. The final section explores the geometric properties of the space .

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Discussion

Authors

Ting Gan

Taja Yaying

Orhan Tuǧ

Journals

Journal of Function Spaces

Actions

Institutions

Jimei University

Bartin University

Quanzhou Normal University

References and Citations

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Some Paranormed Sequence Spaces Which Involve Arithmetic Divisor Sum Function

Key Points

Abstract

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Discussion

Authors

Journals

Actions

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References and Citations

Citation Network

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Discussion

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