On the index and dilations of completely positive semigroups
| dc.creator | Arveson, William | |
| dc.date | 1997-05-25 | |
| dc.date.accessioned | 2026-07-07T09:13:47Z | |
| dc.date.available | 2026-07-07T09:13:47Z | |
| dc.description | It is known that every semigroup of normal completely positive maps $P = {P_t: t\geq 0}$ of $B(H)$, satisfying $P_t(1) = 1$ for every $t\geq 0$, has a minimal dilation to an E_0-semigroup acting on $B(K)$ for some Hilbert space K containing H. The minimal dilation of P is unique up to conjugacy. In a previous paper a numerical index was introduced for semigroups of completely positive maps and it was shown that the index of P agrees with the index of its minimal dilation to an E_0-semigroup. However, no examples were discussed, and no computations were made. In this paper we calculate the index of a unital completely positive semigroup whose generator is a bounded operator $ L: B(H)\to B(H) $ in terms of natrual structures associated with the generator. This includes all unital CP semigroups acting on matrix algebras. We also show that the minimal dilation of the semigroup $P={\exp{tL}: t\geq 0}$ to an \esg\ is is cocycle conjugate to a CAR/CCR flow. | |
| dc.description | 31 pp. AMS-TeX 2.0 | |
| dc.identifier | https://arxiv.org/abs/funct-an/9705006 | |
| dc.identifier | http://arxiv.org/abs/funct-an/9705006 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/152449 | |
| dc.subject | Functional Analysis | |
| dc.subject | Operator Algebras | |
| dc.title | On the index and dilations of completely positive semigroups | |
| dc.type | text |