Analysis of real rank zero in C*-algebras reveals key K-theoretic properties and implications for infinite inclusions.
We introduce a notion of real rank zero for inclusions of C*-algebras. After showing that our definition has many equivalent characterisations, we offer a complete description of the commutative case. We provide permanence and K-theoretic properties of inclusions of real rank zero and prove that a large class of full infinite inclusions have real rank zero.
No takes yet. Share an insight, caveat, or question.
Gabe et al. (2025) studied this question.
Synapse has enriched 3 closely related papers on similar clinical questions. Consider them for comparative context: