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Journal of Operator Theory

Volume 63, Issue 1, Winter 2010  pp. 85-100.

The C-algebras qAK and S2AK are asymptotically equivalent

Authors Tatiana Shulman
Author institution: Department of Mathematical Sciences, University of Copenhagen, Copenhagen, 2100, Denmark

Summary:  Let A be a separable C-algebra. We prove that its stabilized second suspension S2AK and the C-algebra qAK constructed by Cuntz in the framework of his picture of KK-theory are asymptotically equivalent. This means that there exists an asymptotic morphism from S2AK to qAK and an asymptotic morphism from qAK to S2AK whose compositions are homotopic to the identity maps. This result yields an easy description of the natural transformation from KK-theory to E-theory. Also by Loring's result any asymptotic morphism from \qC to any C-algebra B is homotopic to a -homomorphism. We prove that the same is true when \C is replaced by any nuclear C-algebra A and when B is stable.


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