A study on some paranormed sequence spaces due to Lambda–Pascal matrix

Abstract

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.