Nowhere scattered multiplier algebras

Abstract

We study sufficient conditions under which a nowhere scattered C*-algebra $A$ has a nowhere scattered multiplier algebra $\mathcal{M}(A)$, that is, we study when $\mathcal{M}(A)$ has no nonzero, elementary ideal-quotients. In particular, we prove that a $\sigma$-unital C*-algebra $A$ of finite nuclear dimension, or real rank zero, or stable rank one with $k$-comparison, is nowhere scattered if and only if $\mathcal{M}(A)$ is.

arXiv comment22 pages

References in corpus (4)

• Tensor products and regularity properties of Cuntz semigroups
• Divisibility properties for C*-algebras
• Nuclear dimension and Z-stability of non-simple C*-algebras
• Cuntz semigroups of ultraproduct C*-algebras