Journal of Operator Theory

Volume 49, Issue 1, Winter 2003 pp. 77-84.

Real structure in purely infinite $C^\ast$-algebras

Authors: P.J. Stacey
Author institution: Department of Mathematics, La Trobe University, Bundoora, Victoria, 3083 Australia

Summary: It is shown that if the complexification of a real $C^\ast$-algebra $A$ is purely infinite then $A$ shares this property. The converse is also established when the complexification is simple, unital and has real rank zero.

Keywords: $C^\ast$-algebras, purely infinite, real structure, involutory $\ast$-antiautomorphism

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