Rigged Hilbert Spaces associated with Misra-Prigogine-Courbage Theory of Irreversibility
| dc.creator | Ordonez, Adolfo R. | |
| dc.date | 2000-06-13 | |
| dc.date.accessioned | 2026-07-07T04:27:51Z | |
| dc.date.available | 2026-07-07T04:27:51Z | |
| dc.description | It is proved that, in the Misra-Prigogine-Courbage Theory of Irreversibility using the Internal Time superoperator, fixing its associated non-unitary transformation $Λ$, amounts to rigging the corresponding Hilbert-Liouville space. More precisely, it is demonstrated that any $Λ$ determinates three canonical riggings of the Liouville space $\QTR{cal}{L}$: a first one with a Hilbert space with a norm greater than the relative one from $\QTR{cal}{L}$; a second one with a $σ$-Hilbertian space, which is a Köthe space if $Λ$ is compact and is a nuclear space if $Λ$ has certain nuclear properties; and finally a third one with a smaller $σ$-Hilbertian space with a still stronger topology which is nuclear if $Λ^{n}$ is Hilbert-Schmidt, for some positive integer n. Viceversa: any rigging of this type, originated in a dynamical system having an Internal Time superoperator, defines a $Λ$ in a canonical way. | |
| dc.description | 10 pages | |
| dc.identifier | https://arxiv.org/abs/math-ph/0006014 | |
| dc.identifier | http://arxiv.org/abs/math-ph/0006014 | |
| dc.identifier | Phys. A 252 (1998) 362-376 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/56569 | |
| dc.subject | Mathematical Physics | |
| dc.title | Rigged Hilbert Spaces associated with Misra-Prigogine-Courbage Theory of Irreversibility | |
| dc.type | text |