On expansion of quantum quadratic stochastic processes into fibrewise Markov processes defined on von Neumann algebras

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16 Citations (Scopus)

Abstract

We give an expansion of a quantum quadratic stochastic process (q. q. s. p.) into a so-called fibrewise Markov process and prove that, conversely, such an expansion uniquely determines the quantum quadratic stochastic process. As an application, we give a criterion (in terms of this expansion) for the q. q. s. p. to satisfy the ergodic principle. Using this result, we prove that a q. q. s. p. satisfies the ergodic principle if and only if the associated Markov process satisfies this principle. The expansion obtained is used to introduce a new notion of conjugacy of two q. q. s. p.'s and to study the relation between this notion and the ergodic principle.

Original languageEnglish
Pages (from-to)1009-1024
Number of pages16
JournalIzvestiya Mathematics
Volume68
Issue number5
DOIs
Publication statusPublished - Sep 2004
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics(all)

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