DT-operators and decomposability of Voiculescu's circular operator
| dc.creator | Dykema, Ken | |
| dc.creator | Haagerup, Uffe | |
| dc.date | 2002-05-08 | |
| dc.date.accessioned | 2026-07-07T04:48:20Z | |
| dc.date.available | 2026-07-07T04:48:20Z | |
| dc.description | The DT-operators are introduced, one for every pair (μ,c) consisting of a compactly supported Borel probability measure μon the complex plane and a constant c>0. These are operators on Hilbert space that are defined as limits in *-moments of certain upper triangular random matrices. The DT-operators include Voiculescu's circular operator and elliptic deformations of it, as well as the circular free Poisson operators. We show that every DT-operator is strongly decomposable. We also show that a DT-operator generates a II_1-factor, whose isomorphism class depends only on the number and sizes of atoms of μ. Those DT-operators that are also R-diagonal are identified. For a quasi-nilpotent DT-operator T, we find the distribution of T^*T and a recursion formula for general *-moments of T. | |
| dc.description | 58 pages | |
| dc.identifier | https://arxiv.org/abs/math/0205077 | |
| dc.identifier | http://arxiv.org/abs/math/0205077 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/64008 | |
| dc.subject | Operator Algebras | |
| dc.subject | 46L54; 47C15 | |
| dc.title | DT-operators and decomposability of Voiculescu's circular operator | |
| dc.type | text |