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.