ABSTRACT
13.1 From this chapter on we shall be concerned with holomorphic maps defined on complex normed spaces E and taking values in a complex Banach space F. Theory of holomorphy is distinguished from that of (real) analytic functions. One of the most important distinctions is that holomorphic mappings have the Cauchy integral representation. Here it will be shown that a substantial portion in the elements of complex function theory can be extended to normed spaces in light of the Cauchy integral formula. We also study here Cartan’s uniqueness theorem, some aspects of homogeneous domains, and fixed points of holomorphic mappings.
