Rotund Gateaux smooth norms which are not locally uniformly rotund
Functional Analysis
2024-02-28 v2
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.
Cite
@article{arxiv.2303.01833,
title = {Rotund Gateaux smooth norms which are not locally uniformly rotund},
author = {Carlo Alberto De Bernardi and Jacopo Somaglia},
journal= {arXiv preprint arXiv:2303.01833},
year = {2024}
}