Regularity for stably projectionless, simple C*-algebras

Details Regularity for stably projectionless, simple C*-algebras Regularity for stably projectionless, simple C*-algebras

2011-10-06

arxiv.org/abs/1110.1390v1

Mathematics

Operator Algebras

25 pages

Scientific paper

This paper explores the following regularity properties and their relationships for simple, not-necessarily-unital C*-algebras: (i) Jiang-Su stability, (ii) Unperforation in the Cuntz semigroup, and (iii) slow dimension growth (applying only in the case that the C*-algebra is approximately subhomogeneous). An example is given of a simple, separable, nuclear, stably projectionless C*-algebra whose Cuntz semigroup is not almost unperforated. This example is in fact approximately subhomogeneous. It is also shown that, in contrast to this example, when an approximately subhomogeneous simple C*-algebra has slow dimension growth, its Cuntz semigroup is necessarily almost unperforated.

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