2000/06/13 by Adolfo R. Ordonez
Physics and Astronomy · Mathematics · #math-ph #math.MP
published as Phys. A 252 (1998) 362-376 · 10 pages
arxiv created 2000/06/13 · arxiv updated 2009/11/30
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 \QTRcalL: a first one with a Hilbert space with a norm greater than the relative one from \QTRcalL; 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 Λn 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.