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Article Dans Une Revue J. Op. Th. Année : 2004

Global Glimm halving for C*-bundles,

Résumé

Local and global definitions of pure infiniteness for a \cst-algebra $A$ are compared, and equivalence between them is obtained if the primitive ideal space of $A$ is Hausdorff and of finite dimension, if $A$ has real rank zero, or if $A$ is approximately divisible. Sufficient criteria are given for local pure infiniteness of tensor products. They yield that exact simple tensorially non-prime \cst-algebras are purely infinite if they have no semi-finite lower semi-continuous trace. One obtains that $A$ is isomorphic to $A\ot \Oinf$ if $A$ is (1-)purely infinite, separable, stable, nuclear and $\textrm{Prim}(A)$ is a Hausdorff space (not necessarily of finite dimension).
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Dates et versions

hal-00922860 , version 1 (03-01-2014)

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  • HAL Id : hal-00922860 , version 1

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Etienne Blanchard, Eberhard Kirchberg. Global Glimm halving for C*-bundles,. J. Op. Th., 2004, 52, pp.385---420. ⟨hal-00922860⟩
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