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Factorization in commutative Banach algebras

Volume 259 / 2021

H. G. Dales, J. F. Feinstein, H. L. Pham Studia Mathematica 259 (2021), 79-120 MSC: Primary 46J10; Secondary 46J15, 46J20, 46J45. DOI: 10.4064/sm191216-22-7 Published online: 1 February 2021


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.


  • H. G. DalesDepartment of Mathematics and Statistics
    Lancaster University
    Lancaster LA1 4YF, United Kingdom
  • J. F. FeinsteinSchool of Mathematical Sciences
    University of Nottingham
    Nottingham, NG7 2RD, United Kingdom
  • H. L. PhamSchool of Mathematics and Statistics
    Victoria University of Wellington
    Wellington 6140, New Zealand

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