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

• Autorzy: H. Arizmendi-Peimbert , A. Carrillo-Hoyo , A. Garcı́a
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

spectral synthesis; strict topology; closed ideals; topological divisors of zero

• Wydawca: Polish Mathematical Society
• Czasopismo: Commentationes Mathematicae
• Rocznik: 2008
• Tom: 48
• Numer: 2

Daty

wydano

2008

online

2017-12-19

Twórcy

autor

H. Arizmendi-Peimbert

autor

A. Carrillo-Hoyo

autor

A. Garcı́a

Identyfikatory

DOI

10.14708/cm.v48i2.5266