International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 30, Pages 1883-1897
doi:10.1155/S0161171203210590

Topological duals of some paranormed sequence spaces

Nandita Rath

Department of Mathematics and Statistics, University of Western Australia, Nedlands 6907, WA, Australia

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.