Institute of Mathematics and Informatics Bulgarian Academy of Sciences
Serdica Mathematical Journal, Vol. 22, No 1, (1996), 33p-38p
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.