Determining boundary sets of bounded symmetric domains

We consider bounded symmetric domains in complex Banach spaces. It is known that each of these domains can be realized as open unit ballD of a uniquely determined complex Banach spaceE and that every biholomorphic automorphismg ofD extends holomorphically to the closure ofD inE. We study subsetsS of (and in particular of the boundary ϖD) such that every automorphismg is already uniquely determined by its values onS. We also consider subsetsS with the analogue topological property: For every sequence (g _n ) of automorphisms converging uniformly onS tog the convergence is already uniform onD. Supported by Acción Integrada Hispano-Alemana Supported by Xunta de Galicia, project Xuga 20702 B 90