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 -