ESTERLE, Jean

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ESTERLE, Jean
Institut de Mathématiques de Bordeaux [IMB]

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H.G. Dales and the author showed independently that if the continuum hypothesis is assumed then discontinuous algebra norms do exist on C(K) for every compact space K, and it is known that every ideal I of C(K) which is closed with respect to such a norm is equal to the intersection of all closed prime ideals of C(K) containing I. The continuity ideal I(q) of a discontinuous algebra norm q on C(K) is the largest ideal I of C(K) such that the restriction of q to I is continuous. It is known that I(q) is the intersection of all elements of the set Prim(q) of nonmaximal prime ideals which are closed with respect to q. If K is an F-space, then Prim(q) is a finite union of chain of prime ideals, but Pham proved that this is not true in general. The purpose of the paper is to make some progress towards a complete description of the continuity ideals and of the sets Prim(q).< Réduire

Mots clés en anglais

banach algebra

continuum hypothesis

continuity ideal

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Closed prime ideals for discontinuous algebra seminorms on C(K)

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Résumé en anglais

Mots clés en anglais

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