Rigged Hilbert spaces associated with Misra–Prigogine–Courbage theory of irreversibility

Adolfo R Ordóñez

Physica A: Statistical Mechanics and its Applications, 1998, vol. 252, issue 3, 362-376

Abstract: 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 determines three canonical riggings of the Liouville space L: first one with a Hilbert space with a norm greater than the relative one from 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 Λn is Hilbert–Schmidt, for some positive integer n. In contrast any rigging of this type, originated in a dynamical system having an Internal Time superoperator, defines a Λ in a canonical way.

Date: 1998
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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:252:y:1998:i:3:p:362-376

DOI: 10.1016/S0378-4371(97)00643-2

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