Real rank of extensions of C *-algebras

Journal article, 2024

Given a closed ideal A in a C * -algebra E, we develop techniques to bound the real rank of E in terms of the real ranks of A and E/A. Building on work of Brown, Lin and Zhang, we obtain explicit computations if A belongs to any of the following classes: (1) C * -algebras with real rank zero, stable rank one and vanishing K 1 -group; (2) simple, purely infinite C * -algebras; (3) simple, Z -stable C * -algebras with real rank zero; (4) separable, stable C * -algebras with an approximate unit of projections and the Corona Factorization Property.