Maximal chains of closed prime ideals for discontinuous algebra norms on C(K)
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | ESTERLE, Jean | |
| dc.date.accessioned | 2024-04-04T02:23:10Z | |
| dc.date.available | 2024-04-04T02:23:10Z | |
| dc.date.created | 2012-06 | |
| dc.date.issued | 2012-12 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/189711 | |
| dc.description.abstractEn | Let K be an infinite compact space, let C(K) be the algebra of continuous complex-valued functions of K, let F be a well-ordered chain of nonmaximal prime ideals of C(K), let I_F be the smallest element of F and let M_F be the unique maximal ideal of C(K) containing the elements of F. Assuming the continuum hypothesis, we show that if |C(K)/IF | is the continuum , and if there exists a sequence (G_n ) of subsets of F U {M_F } stable under unions such that F U {MF } = UG_n , then there exists a discontinuous algebra norm p on C(K) such that the set of all nonmaximal prime ideals of C(K) which are closed with respect to p equals F. | |
| dc.language.iso | en | |
| dc.subject.en | continuum hypothesis | |
| dc.subject.en | prime ideals | |
| dc.subject.en | algebra norm | |
| dc.subject.en | algebra of continuous functions on a Banach space | |
| dc.title.en | Maximal chains of closed prime ideals for discontinuous algebra norms on C(K) | |
| dc.type | Article de revue | |
| dc.subject.hal | Mathématiques [math]/Analyse fonctionnelle [math.FA] | |
| bordeaux.journal | Mathematical Proceedings of the Royal Irish Academy | |
| bordeaux.page | 101-115 | |
| bordeaux.volume | 112A | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.issue | 2 | |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-00773663 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Non spécifiée | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-00773663v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Mathematical%20Proceedings%20of%20the%20Royal%20Irish%20Academy&rft.date=2012-12&rft.volume=112A&rft.issue=2&rft.spage=101-115&rft.epage=101-115&rft.au=ESTERLE,%20Jean&rft.genre=article |
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