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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| Format: | Article |
| Language: | English |
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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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| _version_ | 1850157629860478976 |
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| author | Nandita Rath |
| author_facet | Nandita Rath |
| author_sort | Nandita Rath |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-2c1967d8a2944f68b0e06cf93f089ed9 |
| institution | OA Journals |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2003-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-2c1967d8a2944f68b0e06cf93f089ed92025-08-20T02:24:07ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252003-01-012003301883189710.1155/S0161171203210590Topological duals of some paranormed sequence spacesNandita Rath0Department of Mathematics and Statistics, University of Western Australia, Nedlands 6907, WA, AustraliaLet 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.http://dx.doi.org/10.1155/S0161171203210590 |
| spellingShingle | Nandita Rath Topological duals of some paranormed sequence spaces International Journal of Mathematics and Mathematical Sciences |
| title | Topological duals of some paranormed sequence spaces |
| title_full | Topological duals of some paranormed sequence spaces |
| title_fullStr | Topological duals of some paranormed sequence spaces |
| title_full_unstemmed | Topological duals of some paranormed sequence spaces |
| title_short | Topological duals of some paranormed sequence spaces |
| title_sort | topological duals of some paranormed sequence spaces |
| url | http://dx.doi.org/10.1155/S0161171203210590 |
| work_keys_str_mv | AT nanditarath topologicaldualsofsomeparanormedsequencespaces |