Abstract
We provide, in every infinite -dimensional separable Banach space, an average locally uniformly rotund (and hence rotund) Gateaux smooth renorming which is not locally uniformly rotund. This solves an open problem posed in a recent monograph by A.J. Guirao, V. Montesinos, and V. Zizler.
Lingua originale | English |
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pagine (da-a) | 1689-1701 |
Numero di pagine | 13 |
Rivista | Proceedings of the American Mathematical Society |
Volume | 152 |
DOI | |
Stato di pubblicazione | Pubblicato - 2024 |
Keywords
- ALUR norm
- Gateaux norm
- LUR norm
- Renorming