Calculus on complex Banach spaces (Q798924)

The paper contains nothing new. It is well known that real Banach spaces (instead of complex ones) are the appropriate object for the purpose of differentiation and optimization. This is rediscovered by the authors: they study continuous ''additive'' maps between complex spaces which are simply continuous linear maps on the underlying real spaces. (Proposition 4.3 is true without the assumption that T is balanced).