On Defining AW*-algebras and Rickart C*-algebras
Operator Algebras
2015-01-13 v1
Abstract
Let A be a C*-algebra. It is shown that A is an AW*-algebra if, and only if, each maximal abelian self--adjoint subalgebra of A is monotone complete. An analogous result is proved for Rickart C*-algebras; a C*-algebra is a Rickart C*-algebra if, and only if, it is unital and each maximal abelian self--adjoint subalgebra of A is monotone {\sigma}-complete.
Keywords
Cite
@article{arxiv.1501.02434,
title = {On Defining AW*-algebras and Rickart C*-algebras},
author = {Kazuyuki Saitô and J. D. Maitland Wright},
journal= {arXiv preprint arXiv:1501.02434},
year = {2015}
}
Comments
10 pages