Non-simple purely infinite C*-algebras: the Hausdorff case

Etienne Blanchard (1) , Eberhard Kirchberg (2)

1 IMJ - Institut de Mathématiques de Jussieu
2 HU Berlin - Humboldt-Universität zu Berlin = Humboldt University of Berlin = Université Humboldt de Berlin

A global notion of Glimm halving for \cst-algebras is considered which implies that every non-zero quotient of an algebra with this property is antiliminal. We prove subtriviality and selection results for Banach spaces of sections vanishing at infinity of a continuous field of Banach spaces. We use them to prove the global Glimm halving property for strictly antiliminal \cst-algebras with Hausdorff primitive ideal space of finite dimension. This implies that a \cst-algebra $A$ with Hausdorff primitive ideal space of finite dimension must be purely infinite if its simple quotients are purely infinite.

Domaines: Algèbres d'opérateurs [math.OA]

Etienne Blanchard, Eberhard Kirchberg. Non-simple purely infinite C*-algebras: the Hausdorff case. Journal of Functional Analysis, 2004, 207, pp.461---513. ⟨hal-00922863⟩