TY - JOUR

T1 - On expansion of quantum quadratic stochastic processes into fibrewise Markov processes defined on von Neumann algebras

AU - Mukhamedov, F. M.

PY - 2004/9

Y1 - 2004/9

N2 - 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.

AB - 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.

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U2 - 10.1070/IM2004v068n05ABEH000506

DO - 10.1070/IM2004v068n05ABEH000506

M3 - Article

AN - SCOPUS:33746513254

VL - 68

SP - 1009

EP - 1024

JO - Izvestiya Mathematics

JF - Izvestiya Mathematics

SN - 1064-5632

IS - 5

ER -