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