Topological duals of some paranormed sequence spaces
Summary: Let \(P=(p_{k})\) be a bounded positive sequence and let \(A=(a_{nk})\) be an infinite matrix with all \(a_{nk}\geq 0\). For normed spaces \(E\) and \(E_{k}\), the matrix \(A\) generates the paranormed sequence spaces \([A,P]_{\infty}((E_{k}))\), \([A,P]_{0}((E_{k}))\), and \([A,P]((E))\), which generalise almost all the well-known sequence spaces such as \(c_{0}\), \(c\), \(l_{p}\), \(l_{\infty}\), and \(w_{p}\). In this paper, topological duals of these paranormed sequence spaces are constructed and general representation formulae for their bounded linear functionals are obtained in some special cases of the matrix \(A\).
scientific article; zbMATH DE number 2012525