ESTERLE, Jean

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ESTERLE, Jean
Institut de Mathématiques de Bordeaux [IMB]

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Mathematical Proceedings of the Royal Irish Academy. 2012-12, vol. 112A, n° 2, p. 101-115

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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.< Leer menos

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continuum hypothesis

prime ideals

algebra norm

algebra of continuous functions on a Banach space

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Maximal chains of closed prime ideals for discontinuous algebra norms on C(K)

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