R-diagonal dilation semigroups
| dc.creator | Kemp, Todd | |
| dc.date | 2007-08-19 | |
| dc.date | 2008-02-11 | |
| dc.date.accessioned | 2026-07-07T09:19:42Z | |
| dc.date.available | 2026-07-07T09:19:42Z | |
| dc.description | This paper addresses extensions of the complex Ornstein-Uhlenbeck semigroup to operator algebras in free probability theory. If $a_1,...,a_k$ are $\ast$-free $\mathscr{R}$-diagonal operators in a $\mathrm{II}_1$ factor, then $D_t(a_{i_1}... a_{i_n}) = e^{-nt} a_{i_1}... a_{i_n}$ defines a dilation semigroup on the non-self-adjoint operator algebra generated by $a_1,...,a_k$. We show that $D_t$ extends (in two different ways) to a semigroup of completely positive maps on the von Neumann algebra generated by $a_1,...,a_k$. Moreover, we show that $D_t$ satisfies an optimal ultracontractive property: $\|D_t\colon L^2\to L^\infty\| \sim t^{-1}$ for small $t>0$. | |
| dc.description | 22 pages, 6 figures | |
| dc.identifier | https://arxiv.org/abs/0708.2562 | |
| dc.identifier | http://arxiv.org/abs/0708.2562 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/154488 | |
| dc.subject | Functional Analysis | |
| dc.subject | Operator Algebras | |
| dc.subject | 46L54 | |
| dc.title | R-diagonal dilation semigroups | |
| dc.type | text |