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arXiv · 1501.02434

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

Kazuyuki Saitô·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 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 maximal abelian self--adjoint subalgebra of A is monotone {\sigma}-complete.

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Kazuyuki Saitô, J. D. Maitland Wright. 2015-01-11. On Defining AW*-algebras and Rickart C*-algebras. https://arxiv.org/abs/1501.02434

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