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arXiv · 2310.00663

Ranks of soft operators in nowhere scattered C*-algebras

M. Ali Asadi-Vasfi·Hannes Thiel·Eduard Vilalta
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Abstract

We show that for C*-algebras with the Global Glimm Property, the rank of every operator can be realized as the rank of a soft operator, that is, an element whose hereditary sub-C*-algebra has no nonzero, unital quotients. This implies that the radius of comparison of such a C*-algebra is determined by the soft part of its Cuntz semigroup. Under a mild additional assumption, we show that every Cuntz class dominates a (unique) largest soft Cuntz class. This defines a retract from the Cuntz semigroup onto its soft part, and it follows that the covering dimensions of these semigroups differ by at most $1$.

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M. Ali Asadi-Vasfi, Hannes Thiel, Eduard Vilalta. 2023-10-01. Ranks of soft operators in nowhere scattered C*-algebras. https://arxiv.org/abs/2310.00663

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