Covering Dimension for Nuclear C*-algebras
| dc.creator | Winter, Wilhelm | |
| dc.date | 2001-07-30 | |
| dc.date.accessioned | 2026-07-07T04:42:47Z | |
| dc.date.available | 2026-07-07T04:42:47Z | |
| dc.description | We introduce the completely positive rank, a notion of covering dimension for nuclear $C^*$-algebras and analyze some of its properties. The completely positive rank behaves nicely with respect to direct sums, quotients, ideals and inductive limits. For abelian $C^*$-algebras it coincides with covering dimension of the spectrum and there are similar results for continuous trace algebras. As it turns out, a $C^*$-algebra is zero-dimensional precisely if it is $AF$. We consider various examples, particularly of one-dimensional $C^*$-algebras, like the irrational rotation algebras, the Bunce-Deddens algebras or Blackadar's simple unital projectionless $C^*$-algebra. Finally, we compare the completely positive rank to other concepts of noncommutative covering dimension, such as stable or real rank. | |
| dc.identifier | https://arxiv.org/abs/math/0107218 | |
| dc.identifier | http://arxiv.org/abs/math/0107218 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/61931 | |
| dc.subject | Operator Algebras | |
| dc.subject | Functional Analysis | |
| dc.title | Covering Dimension for Nuclear C*-algebras | |
| dc.type | text |