THE CONNECTION OF A RICKART REAL C*-ALGEBRA WITH ITS ENVELOPING RICKART (COMPLEX) C*-ALGEBRA - Abduxamidova Dilshoda Bayram qizi; Nilufarxon Raxmonova Vaxobjon qizi (QO‘QON UNIVERSITETI XABARNOMASI, 2023)
In the paper Rickart complex and real C*-algebra are consider. For Rickart 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 is a Rickart real C*-algebra. It is shown that there exists a Rickart real C*- algebra whose projection lattice is not complete.