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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Main Author: A. K. Mirmostafaee
Format: Article
Language:English
Published: Wiley 2004-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Online Access:http://dx.doi.org/10.1155/S0161171204205117
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author A. K. Mirmostafaee
author_facet A. K. Mirmostafaee
author_sort A. K. Mirmostafaee
collection DOAJ
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.
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spelling doaj-art-16cb56b3337f4ec28045ae90e9d08b3f2025-02-03T01:33:09ZengWileyInternational 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
spellingShingle A. K. Mirmostafaee
On non-midpoint locally uniformly rotund normability in Banach spaces
International Journal of Mathematics and Mathematical Sciences
title 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_short On non-midpoint locally uniformly rotund normability in Banach spaces
title_sort on non midpoint locally uniformly rotund normability in banach spaces
url http://dx.doi.org/10.1155/S0161171204205117
work_keys_str_mv AT akmirmostafaee onnonmidpointlocallyuniformlyrotundnormabilityinbanachspaces