Antiproximinal Norms in Banach Spaces
✍ Scribed by J.M. Borwein; M. Jiménez-Sevilla; J.P. Moreno
- Publisher
- Elsevier Science
- Year
- 2002
- Tongue
- English
- Weight
- 132 KB
- Volume
- 114
- Category
- Article
- ISSN
- 0021-9045
No coin nor oath required. For personal study only.
📜 SIMILAR VOLUMES
A closed nonvoid subset Z of a Banach space X is called antiproximinal if no point outside Z has a nearest point in Z. The aim of the present paper is to prove that, for a compact Hausdorff space T and a real Banach space E, the Banach space C T E , of all continuous functions defined on T and with
We show that for the Köthe space X = c 0 + 1 (w), equipped with the Luxemburg norm, the set of norm attaining operators from X into any infinite-dimensional strictly convex Banach space Y is not dense in the space of all bounded operators. The same assertion holds for any infinitedimensional L 1 (µ)