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.
Rotund Gâteaux smooth norms which are not locally uniformly rotund
De Bernardi Carlo Alberto;Somaglia Jacopo
2024-01-01
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:
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De Bernardi, Somaglia - Rotund Gateaux smooth norms which are not locally uniformly rotund (arxiv).pdf
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