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On the ideal structure of algebras of star-algebra valued functions


Author: Jorma Arhippainen
Journal: Proc. Amer. Math. Soc. 123 (1995), 381-391
MSC: Primary 46J20; Secondary 46K05
DOI: https://doi.org/10.1090/S0002-9939-1995-1215198-3
MathSciNet review: 1215198
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Abstract: The ideal structure of the algebra $ C(X,A)$ has been studied in many papers under various topological assumptions on the space X and the algebra A. In this paper we shall study the case where X is a completely regular topological space and A is a locally convex star algebra. In such case the structure of closed (proper) ideals can be described not only by using points of X and some family of closed ideals of A, as usual, but also by using points of the carrier space $ \Delta (A)$ of A and some family of closed ideals of $ C(X,A)$ depending on those points and also by using different kind of slice ideals of $ C(X,A)$.


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DOI: https://doi.org/10.1090/S0002-9939-1995-1215198-3
Article copyright: © Copyright 1995 American Mathematical Society