### 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 (m.a.s.a.) 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 m.a.s.a. subalgebra of A is monotone σ-complete.

Original language | English |
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Pages (from-to) | 979-989 |

Number of pages | 11 |

Journal | Quarterly Journal of Mathematics |

Volume | 66 |

Issue number | 3 |

Early online date | 20 May 2015 |

DOIs | |

Publication status | Published - 20 May 2015 |

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## Cite this

Saito, K., & Wright, J. D. M. (2015). On Defining AW*-algebras and Rickart C*-algebras.

*Quarterly Journal of Mathematics*,*66*(3), 979-989. https://doi.org/10.1093/qmath/hav015