THE CONNECTION OF A RICKART REAL C*-ALGEBRA WITH ITS ENVELOPING RICKART (COMPLEX) C*-ALGEBRA
DOI:
https://doi.org/10.54613/ku.v1i1.288Keywords:
C*-algebra; Rickart complex and real C*-algebras; complex and real AW*- algebras.Abstract
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.
Foydalanilgan adabiyotlar:
C.E. Rickart, Banuch algebras with an adjoint operation. Ann. of Math. (2) 47, (1946), 528-550.
I. Kaplansky, Projections in Banach u/(jehra.s. Ann. of Math. (2) 53, (1951), 235-249.
I. Kaplansky, Algebras of type I. Ann. of. Math. (2) 56, (1952), 460-472.
I. Kaplansky, Modules over operator algebras. Amer. J. Math. 75, (1953), 839-858.
B.-R. Li, Real operator algebras. World Scientific Publishing Co. Pte. Ltd. (2003), 241p.
S.K. Berberian, Baer *-rings. Springer-Verlag, Berlin–Heidelberg–N.Y. 1972.
Sh.A. Ayupov, A.A. Rakhimov, Real W*-algebras, Actions of groups and Index theory for real factors. VDM Publishing House Ltd. Beau-Bassin, Mauritius. ISBN 978-3-639-29066-0, (2010), 138p.
Sh.A. Ayupov, A.A. Rakhimov, Sh. M. Usmanov, Jordan, Real and Lie Structures in Operator Algebras. Kluwer Academic Publishers, MAIA, Vol.418, (1997), 235p. DOI:10.1112/S0024609398305457.
Downloads
Published
Iqtiboslik olish
Issue
Section
License
Copyright (c) 2023 QO‘QON UNIVERSITETI XABARNOMASI
This work is licensed under a Creative Commons Attribution 4.0 International License.