Dales, H.G. and Ulger, Ali (2015) Approximate identities in Banach function algebras. Studia Mathematica, 226 (2). pp. 155-187. ISSN 0039-3223
Abstract
In this paper, we shall study contractive and pointwise contractive Banach function algebras, in which each maximal modular ideal has a contractive or pointwise contractive approximate identity, respectively, and we shall seek to characterize these algebras. We shall give many examples, including uniform algebras, that distinguish between contractive and pointwise contractive Banach function algebras. We shall describe a contractiveBanach function algebras which is not equivalent to a uniform algebra. We shall also obtain results about Banach sequence algebras and Banach function algebras that are ideals in their second duals.