Abstract

Let P=(pk) be a bounded positive sequence and let A=(ank) be an infinite matrix with all ank≥0. For normed spaces E and Ek, the matrix A generates the paranormed sequence spaces [A,P]∞((Ek)), [A,P]0((Ek)), and [A,P]((E)), which generalise almost all the well-known sequence spaces such as c0, c, lp, l∞, and wp. 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 matrix A.