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 |
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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 |
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doaj-16cb56b3337f4ec28045ae90e9d08b3f2020-11-24T22:41:29ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252004-01-012004251343134610.1155/S0161171204205117On non-midpoint locally uniformly rotund normability in Banach spacesA. K. Mirmostafaee0Department of Mathematics, Damghan University of Sciences, P.O. Box 36715-364, Damghan, IranWe 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.http://dx.doi.org/10.1155/S0161171204205117 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
A. K. Mirmostafaee |
| spellingShingle |
A. K. Mirmostafaee On non-midpoint locally uniformly rotund normability in Banach spaces International Journal of Mathematics and Mathematical Sciences |
| author_facet |
A. K. Mirmostafaee |
| author_sort |
A. K. Mirmostafaee |
| title |
On non-midpoint locally uniformly rotund normability in Banach spaces |
| title_short |
On non-midpoint locally uniformly rotund normability in Banach spaces |
| title_full |
On non-midpoint locally uniformly rotund normability in Banach spaces |
| title_fullStr |
On non-midpoint locally uniformly rotund normability in Banach spaces |
| title_full_unstemmed |
On non-midpoint locally uniformly rotund normability in Banach spaces |
| title_sort |
on non-midpoint locally uniformly rotund normability in banach spaces |
| publisher |
Hindawi Limited |
| series |
International Journal of Mathematics and Mathematical Sciences |
| issn |
0161-1712 1687-0425 |
| publishDate |
2004-01-01 |
| description |
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. |
| url |
http://dx.doi.org/10.1155/S0161171204205117 |
| work_keys_str_mv |
AT akmirmostafaee onnonmidpointlocallyuniformlyrotundnormabilityinbanachspaces |
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1725702144422576128 |