International Journal of Mathematics and Mathematical Sciences

International Journal of Mathematics and Mathematical Sciences / 2003 / Article

Open Access

Volume 2003 |Article ID 859016 | https://doi.org/10.1155/S0161171203210590

Nandita Rath, "Topological duals of some paranormed sequence spaces", International Journal of Mathematics and Mathematical Sciences, vol. 2003, Article ID 859016, 15 pages, 2003. https://doi.org/10.1155/S0161171203210590

Topological duals of some paranormed sequence spaces

Received01 Oct 2002

Abstract

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.

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.


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