Caracterisation of Frechet differentiability norm for dual complex Banach spaces

Let X be a complex Banach space, in this work we characterize the property of Frechet differentiability for the dual space of X. In the following, we show that if the dual space of X is Gateaux differentiable, then the dual space of Lp(X) has the same property for all p betwwen one and infiniy
Comment: 6 pages