Topological duals of some paranormed sequence spaces
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,...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2003-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171203210590 |
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| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |