Internal time operators and invariant subspaces
نویسنده
چکیده
An exact theory of irreversibility was proposed by Misra, Prigogine and Courbage (MPC) based on a non-unitary similarity transformation Λ mapping reversible dynamics into irreversible ones. In a previous work a characterization of the irreversible dynamics induced by the MPC theory, the structure of the reversible evolutions admitting such type of change of representation and a prototype for the transformations Λ are given on the basis of the Sz.-Nagy-Foiaş dilation theory. Here it is shown that such reversible evolutions are qualified by the existence of internal time operators if and only if they are associated to innovation processes of Kolmogorov type. In such case, the internal time operator generates a unitary group which together with the reversible evolution satisfy the Weyl commutation relation. This is carried out on the basis of the theory of invariant subspaces and the functional calculus derived from the Sz.Nagy-Foiaş theory.
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