The system will be going down for regular maintenance. Please save your work and logout.
Maximal chains of closed prime ideals for discontinuous algebra norms on C(K)
Language
en
Article de revue
This item was published in
Mathematical Proceedings of the Royal Irish Academy. 2012-12, vol. 112A, n° 2, p. 101-115
English Abstract
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 ...Read more >
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.Read less <
English Keywords
continuum hypothesis
prime ideals
algebra norm
algebra of continuous functions on a Banach space
Origin
Hal imported