Factorization in commutative Banach algebras

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

Abstract

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.

Citation

Dales, H. G., Feinstein, J. F., & Pham, H. L. (2021). Factorization in commutative Banach algebras. Studia Mathematica, 259, 79-120. https://doi.org/10.4064/sm191216-22-7

• 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
• Electronic ISSN: 1730-6337
• Publisher: Polskiej Akademii Nauk, Instytut Matematyczny
• Peer Reviewed: Peer Reviewed
• Volume: 259
• Pages: 79-120
• DOI: https://doi.org/10.4064/sm191216-22-7
• Public URL: https://nottingham-repository.worktribe.com/output/5018728
• Publisher URL: https://www.impan.pl/en/publishing-house/journals-and-series/studia-mathematica/online/114059/factorization-in-commutative-banach-algebras