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Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - Factorization in commutative Banach algebras
AU - Dales, G.
AU - Feinstein, J. F.
AU - Pham, Hung
PY - 2021/4/1
Y1 - 2021/4/1
N2 - 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.
AB - 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.
U2 - 10.4064/sm191216-22-7
DO - 10.4064/sm191216-22-7
M3 - Journal article
VL - 259
SP - 79
EP - 120
JO - Studia Mathematica
JF - Studia Mathematica
SN - 0039-3223
ER -