A CONNECTION BETWEEN RICKART REAL C*-ALGEBRA AND ENVELOPING RICKART C*-ALGEBRA

Abstract

In the paper, Rickart complex and real C*-algebra are considered. For Rickart’s real C*-algebra, its connection with the enveloping (complex) C*-algebra is studied. It is shown that the fact that A is a Rickart real C*-algebra does not imply that a complexification A +i A of A is a Rickart (complex) C*-algebra. Proved that if A is a real C*-algebra and A +i A is a Rickart C*-algebra, then A +i A is a Rickart real C*-algebra. It is shown that there exists a Rickart real C*-algebra whose projection lattice is not complete.