DETERMINING BOUNDARY SETS OF BOUNDED SYMMETRICAL DOMAINS

We consider bounded symmetric domains in complex Banach spaces. It is known that each of these domains can be realized as open unit ball D o f a uniquely determined complex Banach space E and that every biholomo rphic automorphism g of D extends holomorphically to the closure ($) o ver bar D of D in E. We study subsets S of ($) over bar D (and in part icular of the boundary partial derivative D) such that every automorph ism g is already uniquely determined by its values on S. We also consi der subsets S with the analogue topological property: For every sequen ce (g(n)) of automorphisms converging uniformly on S to g the converge nce is already uniform on D.