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doi:10.1016/j.ins.2003.07.009 
Copyright © 2003 Elsevier Inc. All rights reserved.
Some new paranormed sequence spaces
Received 18 April 2003;
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Abstract
Maddox defined the sequence spaces ℓ∞(p), c(p) and c0(p) in [Proc. Camb. Philos. Soc. 64 (1968) 335, Quart. J. Math. Oxford (2) 18 (1967) 345]. In the present paper, the sequence spaces a0r(u,p) and acr(u,p) of non-absolute type have been introduced and proved that the spaces a0r(u,p) and acr(u,p) are linearly isomorphic to the spaces c0(p) and c(p), respectively. Besides this, the α-, β- and γ-duals of the spaces a0r(u,p) and acr(u,p) have been computed and their basis have been constructed. Finally, a basic theorem has been given and later some matrix mappings from a0r(u,p) to the some sequence spaces of Maddox and to some new sequence spaces have been characterized.
Author Keywords: Author Keywords: Paranormed sequence space; α-, β- and γ-duals and basis of a sequence space; Matrix mappings
Article Outline
- 1. Preliminaries, background and notation
- 2. The sequence spaces ar0(u,p) and acr(u,p) of non-absolute type
- 3. The basis for the spaces a0r(u,p) and acr(u,p)
- 4. The α-, β- and γ-duals of the spaces a0r(u,p) and acr(u,p)
- 5. Some matrix mappings on the sequence space a0r(u,p)
- [15]
- Acknowledgements
- References
