Factorization in commutative Banach algebras

Dales, G. and Feinstein, J. F. and Pham, Hung (2021) Factorization in commutative Banach algebras. Studia Mathematica, 259. pp. 79-120. ISSN 0039-3223

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Abstract

We consider when a (non-unital) commutative Banach algebra has a variety of factorization properties; we list the (obvious) implications between these properties, and then investigate 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.