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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,
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- Research Article
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- Copyright © The Author(s), 2024. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh
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