International Journal of Mathematics and Mathematical Sciences
Volume 2003 (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 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.
Let be a bounded positive sequence and let
be an infinite matrix with all . For normed spaces and , the matrix generates the
paranormed sequence spaces , , and , which generalise almost
all the well-known sequence spaces such as , , , , and . 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 .