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

2015/01/11 by Saitô, Kazuyuki, Wright, J. D. Maitland
#37B99 #FOS: Mathematics #Operator Algebras (math.OA) #[2010]Primary46L99

paper · doi:10.48550/arxiv.1501.02434

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 σ-complete.

Related

• Abelian Strict Approximation in AW*-Algebras and Weyl-von Neumann Type Theorems
• Tensor products of maximal abelian subalgebras of C*-algebras
• Commutative C^*-algebras and σ-normal morphisms
• Approximately Finite C*-Algebras and Partial Automorphisms
• Structure theory of homologically trivial and annihilator locally C*-algebras