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# Non-simple Purely Infinite C∗-algebras: the Hausdorff Case Etienne Blanchard and Eberhard Kirchberg

@inproceedings{Kirchberg2006NonsimplePI, title={Non-simple Purely Infinite C∗-algebras: the Hausdorff Case Etienne Blanchard and Eberhard Kirchberg}, author={Eberhard Kirchberg}, year={2006} }

- Published 2006

Local and global definitions of pure infiniteness for a C *-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 C *-algebras are purely infinite if they have no semi-finite lower semi-continuous trace. One obtains that A is… CONTINUE READING

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