This paper delves into the examination of algebraic and topological attributes associated with the domains \(c_0(G,q)\) , c(G, q), and \(\ell _\infty (G,q)\) pertaining to the Lambda–Pascal matrix G in Maddox’s spaces \(c_0(q)\) , c(q), and \(\ell _\infty (q)\) , respectively. The determination of the Schauder basis and the computation of \(\alpha \) -, \(\beta \) -, and \(\gamma \) -duals for these Lambda–Pascal paranormed spaces are carried out. The ultimate section is dedicated to elucidating the classification of the matrix classes \((\ell _{\infty }(G,q),\ell _{\infty })\) , \((\ell _{\infty }(G,q),f)\) , and \((\ell _{\infty }(G,q),c)\) , concurrently presenting the characterization of specific other sets of matrix transformations in the space \(\ell _{\infty }(G,q)\) as corollaries derived from the primary outcomes.
