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Approximate identities in Banach function algebras

Research output: Contribution to journalJournal article

Published
<mark>Journal publication date</mark>2015
<mark>Journal</mark>Studia Mathematica
Issue number2
Volume226
Number of pages33
Pages (from-to)155-187
<mark>State</mark>Published
<mark>Original language</mark>English

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.