Group C*-algebras, metrics and an operator theoretic inequality
| dc.creator | Antonescu, Cristina | |
| dc.creator | Christensen, Erik | |
| dc.date | 2002-11-20 | |
| dc.date.accessioned | 2026-07-07T04:53:07Z | |
| dc.date.available | 2026-07-07T04:53:07Z | |
| dc.description | On a discrete group G a length function may implement a spectral triple on the reduced group C*-algebra. Following A. Connes, the Dirac operator of the triple then can induce a metric on the state space of reduced group C*-algebra. Recent studies by M. Rieffel raise several questions with respect to such a metric on the state space. Here it is proven that for a free non Abelian group, the metric on the state space is bounded. Further we propose a relaxation in the way a length function is used in the construction of a metric, and we show that for groups of rapid decay there are many metrics related to a length function which all have all the expected properties. The boundedness result for free groups is based on an estimate of the completely bounded norm of a certain Schur multiplier and on some techniques concerning free groups due to U. Haagerup. At the end we have included a noncommutative version of the Arzela-Ascoli Theorem. | |
| dc.description | 15 pages | |
| dc.identifier | https://arxiv.org/abs/math/0211312 | |
| dc.identifier | http://arxiv.org/abs/math/0211312 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/65724 | |
| dc.subject | Operator Algebras | |
| dc.subject | Primary 46L10, 46L35; Secondary 46L07, 46L85, 47L25 | |
| dc.title | Group C*-algebras, metrics and an operator theoretic inequality | |
| dc.type | text |