On the Domain of the Pell-Lucas Matrix in the Spaces c and c_0
DOI:
https://doi.org/10.56405/dngcrj.2025.10.01.06Keywords:
Pell-Lucas numbers, Sequence space, Schauder basis, CompactnessAbstract
In this study, we introduce new Banach sequence spaces $c(\Theta), c_0(\Theta)$, defined via a regular infinite matrix $ \Theta = (\lambda_{nk})$, where
\[
\Theta_{nk} =
\begin{cases}
\dfrac{2\lambda_k}{3\lambda_n+\lambda_{n-1}} & 0 \leq k \leq n, \\
0, & k > n,
\end{cases}
\]
and \({\lambda_{nk}}\) represents the Pell–Lucas number sequence. The study primarily focuses on exploring the fundamental properties and inclusion relationships of the corresponding sequence spaces, establishing a Schauder basis, and determining their $\alpha$-, $\beta$-, and $\gamma$-duals. In addition, the work investigates the compactness of matrix operators acting on these associated sequence spaces.
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Copyright (c) 2025 Shiva Shah
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