Topological duals of some paranormed sequence spaces

Nandita Rath

International Journal of Mathematics and Mathematical Sciences, 2003, vol. 2003, 1-15

Abstract:

Let P = ( p k ) be a bounded positive sequence and let A = ( a n k ) be an infinite matrix with all a n k ≥ 0 . For normed spaces E and E k , the matrix A generates the paranormed sequence spaces [ A , P ] ∞ ( ( E k ) ) , [ A , P ] 0 ( ( E k ) ) , and [ A , P ] ( ( E ) ) , which generalise almost all the well-known sequence spaces such as c 0 , c , l p , l ∞ , and w p . 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 .

Date: 2003
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:859016

DOI: 10.1155/S0161171203210590

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