Commutators of free random variables
| dc.creator | Nica, Alexandru | |
| dc.creator | Speicher, Roland | |
| dc.date | 1996-12-10 | |
| dc.date.accessioned | 2026-07-07T09:13:39Z | |
| dc.date.available | 2026-07-07T09:13:39Z | |
| dc.description | Let A be a unital $C^*$-algebra, given together with a specified state $ϕ:A \to C$. Consider two selfadjoint elements a,b of A, which are free with respect to $ϕ$ (in the sense of the free probability theory of Voiculescu). Let us denote $c:=i(ab-ba)$, where the i in front of the commutator is introduced to make c selfadjoint. In this paper we show how the spectral distribution of c can be calculated from the spectral distributions of a and b. Some properties of the corresponding operation on probability measures are also discussed. The methods we use are combinatorial, based on the description of freeness in terms of non-crossing partitions; an important ingredient is the notion of R-diagonal pair, introduced and studied in our previous paper funct-an/9604012. | |
| dc.description | LaTeX, 38 pages with 2 figures | |
| dc.identifier | https://arxiv.org/abs/funct-an/9612001 | |
| dc.identifier | http://arxiv.org/abs/funct-an/9612001 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/152404 | |
| dc.subject | Functional Analysis | |
| dc.subject | Operator Algebras | |
| dc.subject | Quantum Algebra | |
| dc.title | Commutators of free random variables | |
| dc.type | text |