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A spectral synthesis property for \(C_b(X, \Beta)\)

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Arizmendi-Peimbert H., Carrillo-Hoyo A., Garcı́a A.

Commentationes Mathematicae

2008

tom 48

nr 2

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.

Ograniczanie wyników

1 Commentationes Mathematicae

1 Arizmendi-Peimbert H.

1 Carrillo-Hoyo A.

1 Garcı́a A.

1 2008

Wyniki wyszukiwania

A spectral synthesis property for \(C_b(X, \Beta)\)