The algebraic structure of homogeneous balls
In this chapter we will present the main ideas of the theory of homogeneous balls and bounded symmetric domains and the algebraic structure associated with them. The domains will be domains in complex Banach spaces and their homogeneity and symmetry will be with respect to analytic (called also holomorphic) maps. Thus we will start with the definition and study of the analytic mappings on Banach spaces. Next we will consider the group of analytic automorphisms Aut a (D) of a bounded domain D and show that the elements of this group are uniquely defined by their value and the value of their derivative at some point.
KeywordsBanach Space Unit Ball Symmetric Space Jordan Algebra Triple Product
Unable to display preview. Download preview PDF.