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arXiv · 2304.14007

Nowhere scattered multiplier algebras

Eduard Vilalta
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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.

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Eduard Vilalta. 2023-04-27. Nowhere scattered multiplier algebras. https://doi.org/10.1017/prm.2023.123

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