Geodesic
A spectral synthesis property for \(C_b(X, \Beta)\)
Commentationes Mathematicae, Tome 48 (2008) no. 2, pp. 121-127.

Voir la notice de l'article provenant de la source Annales Societatis Mathematicae Polonae Series

Let \((C_b (X) , \Beta)\) be the algebra of all continuous bounded real or complex valued functions defined on a completely regular Hausdorff space \(X\) with the usual algebraic operations and with the strict topology \(\Beta\). It is proved that \((C_b (X) , \Beta)\) has a spectral synthesis, i.e. every of its closed ideals is an intersection of closed maximal ideals of codimension 1. We give one necessary and two sufficient conditions over \(X\) in order that \((C_b (X) , \Beta)\) has no proper non-zero closed principal ideals. Moreover if \(X\) satisfy any of these two conditions and is also a k-space, then any non zero element of \(C_b(X)\) is invertible or a topological divisor of zero.
DOI : 10.14708/cm.v48i2.5266
Mots-clés : spectral synthesis, strict topology, closed ideals, topological divisors of zero 
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H. Arizmendi-Peimbert; A. Carrillo-Hoyo; A. Garcı́a. A spectral synthesis property for \(C_b(X, \Beta)\). Commentationes Mathematicae, Tome 48 (2008) no. 2, pp.  121-127. doi : 10.14708/cm.v48i2.5266. http://geodesic.mathdoc.fr/articles/10.14708/cm.v48i2.5266/

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