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

Kazuyuki Saito, J. D. Maitland Wright

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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 languageEnglish
Pages (from-to)979-989
Number of pages11
JournalQuarterly Journal of Mathematics
Volume66
Issue number3
Early online date20 May 2015
DOIs
Publication statusPublished - 20 May 2015

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