Wydawnictwa / Czasopisma IMPAN / Studia Mathematica / Wszystkie zeszyty

Streszczenie

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, $\mathcal Z$-stable $C^*$-algebras with real rank zero; (4) separable, stable $C^*$-algebras with an approximate unit of projections and the Corona Factorization Property.