A spectral synthesis property for C_b (X, β)

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

Abstrakty

EN

Let (Cb (X) , ) 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 . It is proved that (Cb (X) , β) 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 (Cb (X) , β) 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 Cb (X) is invertible or a topological divisor of zero.

Słowa kluczowe

EN

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

• Wydawca: Polskie Towarzystwo Matematyczne
• Czasopismo: Commentationes Mathematicae
• Rocznik: 2008
• Tom: Vol. 48, [Z] 2
• Strony: 121--127
• Opis fizyczny: bibliogr. 6 poz.

Twórcy

autor

Arizmendi-Peimbert H.

autor

Carrillo-Hoyo A.

autor

Garcia A.

• Instituto de Matematicas, Universidad Nacional Autónoma de México, Ciudad Universitaria, 04510, México, D.F., México,

Bibliografia

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