Graph \(C^*\)-algebras with real rank zero
A unital \(C^*\)-algebra is said to have real rank zero if the set of invertible self-adjoint elements is dense in the set of all self-adjoint elements. Let \(C^*(E)\) be a graph \(C^*\)-algebra associated to a row-finite directed graph \(E\). In this paper, the authors show that \(C^*(E)\) has real rank zero if and only if \(E\) satisfies a certain loop condition (K).
scientific article; zbMATH DE number 1763772