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 |
Bibliographical note
AcknowledgementsIt is a pleasure to thank Dr A. J. Lindenhovius, whose perceptive questions triggered this paper.