On non-midpoint locally uniformly rotund normability in Banach spaces
We will show that if X is a tree-complete subspace of ℓ∞, which contains c0, then it does not admit any weakly midpoint locally uniformly convex renorming. It follows that such a space has no equivalent Kadec renorming.
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2004-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171204205117 |
| Summary: | We will show that if X is a tree-complete subspace of
ℓ∞, which contains c0, then it does not
admit any weakly midpoint locally uniformly convex
renorming. It follows that such a space has no
equivalent Kadec renorming. |
|---|---|
| ISSN: | 0161-1712 1687-0425 |