Article contents
Nowhere scattered multiplier algebras
Published online by Cambridge University Press: 05 January 2024
Abstract
We study sufficient conditions under which a nowhere scattered $\mathrm {C}^*$-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 $\mathrm {C}^*$
-algebra $A$
of
(i) finite nuclear dimension, or
(ii) real rank zero, or
(iii) stable rank one with $k$
-comparison,
![](https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240104121729565-0175:S0308210523001233:S0308210523001233_inline9.png)
- Type
- Research Article
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- Copyright
- Copyright © The Author(s), 2024. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh
References
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