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A spectral synthesis property for C_b (X, β)

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

Commentationes Mathematicae

2008

Vol. 48, [Z] 2

121-127

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.

The strict topology on topological algebras

Khan L., Mohammad N., Thaheem A.

Demonstratio Mathematica

2005

Vol. 38, nr 4

883--894

In this paper, we define strict, uniform and compact-open topologies on a topological algebra and investigate their properties. These results unify and include several results of other authors.

A simple proof of Kasparov's technical theorem

Djoudi A.

Demonstratio Mathematica

2001

Vol. 34, nr 3

651-657

In this note we use the technic of quasi-central approximate units to give anew simple proof of Kasparov's technical theorem [5, §3. th. 4]. An extended version of the theorem to a finite number of C*-algebras is given and proved. In the end we show that the theorem has implications for the problem of lifting derivations.