A CONNECTION BETWEEN RICKART REAL C*-ALGEBRA AND ENVELOPING RICKART C*-ALGEBRA
A. A. RakhimovFaculty of Mathematics National University of Uzbekistan, Tashkent, UzbekistanN.V. RaxmonovaFaculty of Mathematics, Andijan State University, Andijan, UzbekistanZabidin SallehFaculty of Ocean Engineering Technology and Informatics, Universiti Malaysia Terengganu, Kuala Nerus, Terengganu, Malaysia
ABI
Annotatsiya
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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