What type of dynamics arise in E_0-dilations of commuting quantum Markov process?
| dc.creator | Shalit, Orr | |
| dc.date | 2007-11-19 | |
| dc.date | 2007-11-20 | |
| dc.date.accessioned | 2026-07-07T12:54:29Z | |
| dc.date.available | 2026-07-07T12:54:29Z | |
| dc.description | Let H be a separable Hilbert space. Given two strongly commuting CP_0-semigroups $ϕ$ and $θ$ on B(H), there is a Hilbert space K containing H and two (strongly) commuting E_0-semigroups $α$ and $β$ such that $ϕ_s \circ θ_t (P_H A P_H) = P_H α_s \circ β_t (A) P_H$ for all s,t and all A in B(K). In this note we prove that if $ϕ$ is not an automorphism semigroup then $α$ is cocycle conjugate to the minimal *-endomorphic dilation of $ϕ$, and that if $ϕ$ is an automorphism semigroup then $α$ is also an automorphism semigroup. In particular, we conclude that if $ϕ$ is not an automorphism semigroup and has a bounded generator (in particular, if H is finite dimensional) then $α$ is a type I E_0-semigroup. | |
| dc.description | 9 pages, minor corrections made | |
| dc.identifier | https://arxiv.org/abs/0711.2876 | |
| dc.identifier | http://arxiv.org/abs/0711.2876 | |
| dc.identifier | Infin. Dimens. Anal. Quantum Probab. Relat. Top. 11/3 (2008), 393-403 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/223948 | |
| dc.subject | Operator Algebras | |
| dc.subject | 46L55; 46L57 | |
| dc.title | What type of dynamics arise in E_0-dilations of commuting quantum Markov process? | |
| dc.type | text |