ON CONSTRUCTION OF REAL AW*-FACTORS

Abstract

The paper of the is to initiate the study of real AW*-algebras in the framework of the theory of real C*-algebras and W*-algebras. It happens that in some aspects real AW*-algebras behave unlike complex AW*-algebras and sometimes their properties are completely different also from corresponding properties of real W*-algebras. We prove that if the complexification  of a real C*-algebra A is a (complex) AW*-algebra then A itself is a real AW∗-algebra. By modifying the Takenouchi’s examples of complex non-W*, AW*-factors we show that there exist real non-W*, AW*-factors.