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Factorization in commutative Banach algebras

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<mark>Journal publication date</mark>1/04/2021
<mark>Journal</mark>Studia Mathematica
Number of pages42
Pages (from-to)79-120
Publication StatusPublished
Early online date1/02/21
<mark>Original language</mark>English


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.