On q -Pell sequence spaces: A study of operator ideals and geometric properties
Year: 2025
Type: article
Abstract: The matrix P ( q ) = { Ψ λ μ ( q ) } λ , μ ∈ N , called the q -Pell matrix, with elements determined by P ( q ) = 2 q μ − 1 Ψ μ ( q ) Ψ λ + 1 ( q ) + Ψ λ ( q ) − 1 , if 1 ≤ μ ≤ λ , 0 , if μ > λ . with { Ψ λ ( q ) } representing the q -Pell sequence. Using P ( q ) is defined by Ψ λ ( q ) = ( 1 + q λ + 1 ) Ψ λ − 1 ( q ) + Ψ λ − 2 ( q ) for λ ≥ 2 , Ψ 0 ( q ) = 0 , Ψ 1 ( q ) = 1 . In this context, the Schauder basis is derived for the space ℓ p ( P ( q ) ) for 1 ≤ p ≤ ∞ . The key geometric properties of ℓ p ( P ( q ) ) and ℓ ∞ ( P ( q ) ) , such as the approximation property, the Dunford–Pettis property, the Hahn–Banach extension property, and rotundity, are examined. Finally, the solidity properties of these sequence spaces are studied.
Source: Kuwait Journal of Science
Authors: Shiva Shah, Bipan Hazarika
Institution: Gauhati University
Language: English
Topic: Advanced Banach Space Theory
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $1,100
OpenAlex ID: W4416396343