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
Department of Mathematics and Statistics, University of Western Australia, Nedlands 6907, WA, Australia
Received 1 October 2002
Copyright © 2003 Nandita Rath. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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.