Vector-valued sequence spaces generated by infinite matrices

Nandita Rath

International Journal of Mathematics and Mathematical Sciences, 2001, vol. 26, 1-14

Abstract:

Let A = ( a n k ) be an infinite matrix with all a n k ≥ 0 and P a bounded, positive real sequence. For normed spaces E and E k the matrix A generates paranormed sequence spaces such as [ A , P ] ∞ ( ( E k ) ) , [ A , P ] 0 ( ( E k ) ) , and [ A , P ] ( E ) which generalize almost all the existing sequence spaces, such as l ∞ , c 0 , c , l p , w p , and several others. In this paper, conditions under which these three paranormed spaces are separable, complete, and r -convex, are established.

Date: 2001
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:824723

DOI: 10.1155/S0161171201005166

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