Bulletin of the Australian Mathematical Society

Table of Contents - June 2008 - Volume 77, Issue 03  

Research Article

AMENABILITY FOR REAL C*-ALGEBRAS

NHAN BAO HOa1

a1 Department of Mathematical and Statistical Sciences, La Trobe University, Victoria 3086, Australia (email: honhanbao@yahoo.com)

Abstract

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

  • 46L05

Keywords and phrases

  • real C*-algebra;
  • amenability;
  • completely positive map