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Completely positive maps into corona algebras

Published online by Cambridge University Press:  01 September 2009

DAN Z. KUCEROVSKY  and
P. W. NG
DAN Z. KUCEROVSKY
Affiliation:
Department of Mathematics and Statistics, University of New Brunswick, Fredericton, New Brunswick, E3B 5A3Canada. e-mail: dkucerov@unb.ca
P. W. NG
Affiliation:
University of Louisiana at Lafyette, 217 Doucet Hall P.O. Box 41010 Lafayette, LA, U.S.A. 70504-1010. e-mail: pwn@louisiana.edu
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Abstract

We prove a decomposition theorem similar to the well-known result of Voiculescu's: namely that completely positive maps A → (B)/B factor through a given homomorphism ι: A →(B)/B when the homomorphism ι has a certain infiniteness property.

The algebra B is only assumed to be separable and nonunital; in particular, it is not assumed to be stable. The C*-algebra A is assumed to be separable, unital and nuclear.

Information

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 147 , Issue 2 , September 2009 , pp. 323 - 337
Copyright
Copyright © Cambridge Philosophical Society 2009

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