Approximate identities in Banach function algebras
Volume 226 / 2015
Studia Mathematica 226 (2015), 155-187
MSC: Primary 46B15; Secondary 46B28, 46B42, 47L10.
DOI: 10.4064/sm226-2-3
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 contractive Banach function algebra 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.
