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AMENABILITY FOR REAL C*-ALGEBRAS

Part of: Selfadjoint operator algebras

Published online by Cambridge University Press:  01 June 2008

NHAN BAO HO
NHAN BAO HO*
Affiliation:
Department of Mathematical and Statistical Sciences, La Trobe University, Victoria 3086, Australia (email: [email protected])
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Abstract

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It is shown that the complexification of a positive linear map on a real C*-algebra need not be positive whereas the complexification of a completely positive linear map is completely positive. It is further shown that a real C*-algebra is amenable if and only if its complexification is amenable and that a completely positive linear map is amenable if and only if its complexification is. Finally, a real version of the Choi–Effros lifting theorem is established.

Keywords

real C*-algebraamenabilitycompletely positive map

MSC classification

Secondary: 46L05: General theory of $C^*$-algebras
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 77 , Issue 3 , June 2008 , pp. 509 - 514
Copyright
Copyright © 2008 Australian Mathematical Society

References

[1]Goodearl, R. K., Notes on Real and Complex C *-algebras (Shiva, England, 1982).Google Scholar
[2]Lin, H., An Introduction to the Classification of Amenable C *-algebras (World Scientific, River Edge, NJ, 2001).Google Scholar