Rotund Gateaux smooth norms which are not locally uniformly rotund

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.

References in corpus (2)

• Smooth and polyhedral norms via fundamental biorthogonal systems
• Characterizations of weakly $\mathcal{K}$-analytic and Vašák spaces using projectional skeletons and separable PRI