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arXiv · 2303.01833

Rotund Gateaux smooth norms which are not locally uniformly rotund

Carlo Alberto De Bernardi·Jacopo Somaglia
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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 by A.J. Guirao, V. Montesinos, and V. Zizler.

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BibTeXRIS

Carlo Alberto De Bernardi, Jacopo Somaglia. 2023-03-03. Rotund Gateaux smooth norms which are not locally uniformly rotund. https://doi.org/10.1090/proc/16659

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