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Factorization in commutative Banach algebras

Research output: Contribution to journalJournal article

Forthcoming
<mark>Journal publication date</mark>10/08/2020
<mark>Journal</mark>Studia Mathematica
Number of pages46
Publication StatusAccepted/In press
<mark>Original language</mark>English

Abstract

Let A be a (non-unital) commutative Banach algebra. We consider when A has a variety of factorization properties: we list the (obvious) implications between these properties, and then consider whether any of these implications can be reversed in various classes of commutative Banach algebras. We summarize the known counter-examples to these possible reverse implications, and add further counter-examples. Some results are used to show the existence of a large family of prime ideals in each non-zero, commutative, radical Banach algebra with a dense set of products.