### Abstract

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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*Quarterly Journal of Mathematics*,

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

**On Defining AW*-algebras and Rickart C*-algebras.** / Saito, Kazuyuki; Wright, J. D. Maitland.

Research output: Contribution to journal › Article

*Quarterly Journal of Mathematics*, vol. 66, no. 3, pp. 979-989. https://doi.org/10.1093/qmath/hav015

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TY - JOUR

T1 - On Defining AW*-algebras and Rickart C*-algebras

AU - Saito, Kazuyuki

AU - Wright, J. D. Maitland

N1 - Acknowledgements It is a pleasure to thank Dr A. J. Lindenhovius, whose perceptive questions triggered this paper.

PY - 2015/5/20

Y1 - 2015/5/20

N2 - 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.

AB - 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.

U2 - 10.1093/qmath/hav015

DO - 10.1093/qmath/hav015

M3 - Article

VL - 66

SP - 979

EP - 989

JO - Quarterly Journal of Mathematics

JF - Quarterly Journal of Mathematics

SN - 0033-5606

IS - 3

ER -