DOES A NON-LIPSCHITZ FUNCTION OPERATE ON A NON-TRIVIAL BANACH FUNCTION ALGEBRA?

Abstract

We show a property of a normal Banach function algebra on which a non-Lipschitz function operates. An example of a non-trivial normal Banach function algebra such that the operating functions are not necessarily locally Lipschitzian is given. We also show a sufficient condition in terms of the operating functions for a normal Banach function algebra to coincide with the algebra of all complex-valued continuous functions.