Representable Banach Spaces and Uniformly Gateaux-Smooth Norms
Frontisi, Julien (1996)
Serdica Mathematical Journal
Similarity:
It is proved that a representable non-separable Banach space does not admit uniformly Gâteaux-smooth norms. This is true in particular for C(K) spaces where K is a separable non-metrizable Rosenthal compact space.