Bulletin of the Australian Mathematical Society

Research Article

Each weakly countably determined Asplund space admits a Fréchet differentiable norm

M. Fabiana1

a1 Sibeliova 49, 162 00 Prague 6, Czechoslovakia

If au Asplund space is weakly countably determined, then it admits an equivalent Fréchet differentiable norm and is weakly compactly generated. If on an Asplund space there exists an equivalent Gâteaux differentiable norm, then its dual has a projectional resolution of identity.

(Received October 29 1986)