A CONNECTION BETWEEN RICKART REAL C*-ALGEBRA AND ENVELOPING RICKART C*-ALGEBRA
DOI:
https://doi.org/10.46754/jmsi.2022.12.003Keywords:
C*-algebra, Rickart complex and real C*-algebras, complex and real AW*-algebrasAbstract
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.
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