Endomorphisms of Pointwise Lipschitz Algebras

Abstract

© 2020, Malaysian Mathematical Sciences Society and Penerbit Universiti Sains Malaysia. Let (X, d) be a compact metric space. Then, the normed algebra of pointwise Lipschitz functions on X is denoted by Lip pw(X, d). We study and characterize the completeness of these algebras and obtain a necessary and sufficient condition for such an algebra to be complete. We then investigate the endomorphisms of Lip pw(X, d) by considering their associated self-maps. A necessary and sufficient condition is given for these operators to be compact. Moreover, we discuss relations between Lip pw(X, d) and other normed function algebras.