- Tytuł:
- A spectral synthesis property for \(C_b(X, \Beta)\)
- Autorzy:
-
Arizmendi-Peimbert, H.
Carrillo-Hoyo, A.
Garcı́a, A. - Powiązania:
- https://bibliotekanauki.pl/articles/745757.pdf
- Data publikacji:
- 2008
- Wydawca:
- Polskie Towarzystwo Matematyczne
- Tematy:
-
spectral synthesis
strict topology
closed ideals
topological divisors of zero - Opis:
- 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.
- Źródło:
-
Commentationes Mathematicae; 2008, 48, 2
0373-8299 - Pojawia się w:
- Commentationes Mathematicae
- Dostawca treści:
- Biblioteka Nauki
Artykuł