On the Domain of the Pell-Lucas Matrix in the Spaces c and c_0

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.