a1 Department of Mathematical and Statistical Sciences, La Trobe University, Victoria 3086, Australia (email: firstname.lastname@example.org)
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.
(Received November 26 2007)
2000 Mathematics subject classification
Keywords and phrases