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Factorization in commutative Banach algebras

Dales, H G; Feinstein, J F; Pham, H L

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H G Dales

H L Pham


Let A be a (non-unital) commutative Banach algebra. We consider when A has a variety of factorization properties: we list the (ob-vious) implications between these properties, and then consider whether any of these implications can be reversed in various classes of commu-tative Banach algebras. We summarize the known counterexamples to these possible reverse implications, and add further counterexamples. 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.


Dales, H. G., Feinstein, J. F., & Pham, H. L. (2021). Factorization in commutative Banach algebras. Studia Mathematica, 259, 79-120.

Journal Article Type Article
Acceptance Date Jul 20, 2020
Online Publication Date Feb 1, 2021
Publication Date 2021
Deposit Date Nov 5, 2020
Publicly Available Date Feb 1, 2021
Journal Studia Mathematica
Print ISSN 0039-3223
Publisher Polskiej Akademii Nauk, Instytut Matematyczny
Peer Reviewed Peer Reviewed
Volume 259
Pages 79-120
Public URL
Publisher URL


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