Nowhere scattered -algebras
Hannes Thiel
Kiel University, GermanyEduard Vilalta
Universitat Autònoma de Barcelona, Spain
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Abstract
We say that a -algebra is nowhere scattered if none of its quotients contains a minimal open projection. We characterize this property in various ways, by topological properties of the spectrum, by divisibility properties in the Cuntz semigroup, by the existence of Haar unitaries for states, and by the absence of nonzero ideal-quotients that are elementary, scattered or type . Under the additional assumption of real rank zero or stable rank one, we show that nowhere scatteredness implies even stronger divisibility properties of the Cuntz semigroup.
Cite this article
Hannes Thiel, Eduard Vilalta, Nowhere scattered -algebras. J. Noncommut. Geom. 18 (2024), no. 1, pp. 231–263
DOI 10.4171/JNCG/526