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.
De Bernardi, C. A., Somaglia, J., ROTUND GÂTEAUX SMOOTH NORMS WHICH ARE NOT LOCALLY UNIFORMLY ROTUND, <<PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY>>, 2024; 152 (4): 1689-1701. [doi:10.1090/proc/16659] [https://hdl.handle.net/10807/270755]
ROTUND GÂTEAUX SMOOTH NORMS WHICH ARE NOT LOCALLY UNIFORMLY ROTUND
De Bernardi, Carlo Alberto
;
2024
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.
File in questo prodotto:
| File | Dimensione | Formato | |
|---|---|---|---|
|
S0002-9939-2024-16659-4.pdf
accesso aperto
Tipologia file ?:
Versione Editoriale (PDF)
Note: https://www.ams.org/publications/journals/open-access/open-access
Licenza:
Creative commons
Dimensione
231.13 kB
Formato
Adobe PDF
|
231.13 kB | Adobe PDF | Visualizza/Apri |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
