A Urysohn-type theorem and the Bishop-Phelps-Bollobas theorem for holomorphic functions

A Urysohn-type theorem is introduced for a subalgebra of the algebra C-b (Omega) of all bounded complex-valued continuous functions on a Hausdorff topological space Omega. With use of this theorem, it is shown that a type of the Bishop-Phelps-Bollobas theorem holds for certain classes of holomorphic functions on the unit ball of a complex Banach space X if X is either a locally uniformly convex space or a locally c-uniformly convex, order-continuous sequence space. (C) 2019 Elsevier Inc. All rights reserved.