Resolvents of R-Diagonal Operators
| dc.creator | Haagerup, Uffe | |
| dc.creator | Kemp, Todd | |
| dc.creator | Speicher, Roland | |
| dc.date | 2008-11-19 | |
| dc.date.accessioned | 2026-07-07T10:19:30Z | |
| dc.date.available | 2026-07-07T10:19:30Z | |
| dc.description | We consider the resolvent $(λ-a)^{-1}$ of any $R$-diagonal operator $a$ in a $\mathrm{II}_1$-factor. Our main theorem gives a universal asymptotic formula for the norm of such a resolvent. En route to its proof, we calculate the $R$-transform of the operator $|λ-c|^2$ where $c$ is Voiculescu's circular operator, and give an asymptotic formula for the negative moments of $|λ-a|^2$ for any $R$-diagonal $a$. We use a mixture of complex analytic and combinatorial techniques, each giving finer information where the other can give only coarse detail. In particular, we introduce {\em partition structure diagrams}, a new combinatorial structure arising in free probability. | |
| dc.description | 29 pages, 12 figures, used gastex.sty | |
| dc.identifier | https://arxiv.org/abs/0811.3125 | |
| dc.identifier | http://arxiv.org/abs/0811.3125 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/174531 | |
| dc.subject | Operator Algebras | |
| dc.subject | Functional Analysis | |
| dc.subject | 46L54, 46L53 | |
| dc.title | Resolvents of R-Diagonal Operators | |
| dc.type | text |