On boundaries for spaces of holomorphic functions on the unit ball of a Banach space

摘要

If Ω is a topological space, a subset S ∈ Ω. is a boundary for an algebra A C ∈_b (Ω) if ‖f‖ sups ES |f (s) | for every f ∈ A. For a complex Banach space X, let A_b(B_X) be the Banach algebra of all complex valued functions defined on the closed unit ball B_X of X which are bounded and continuous on B_X and holomorphic on the interior of B_X, endowed with the sup norm, and let A_u (B_X) be the Banach subalgebra of all complex valued functions defined on B_X which are uniformly continuous on B_X and holomorphic on the interior of B_X. In this paper we survey previous results about the boundaries of these algebras for some classical Banach spaces X.