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International Journal of Mathematics and Mathematical Sciences
Volume 2003, Issue 30, Pages 1883-1897

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 Hindawi Publishing Corporation. 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.


Let P=(pk) be a bounded positive sequence and let A=(ank) be an infinite matrix with all ank0. 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.