Markovian processes on mutually commuting von Neumann algebras

Cecchini, Carlo. "Markovian processes on mutually commuting von Neumann algebras." Banach Center Publications 43.1 (1998): 111-118. <http://eudml.org/doc/208830>.

@article{Cecchini1998,
abstract = {The aim of this paper is to study markovianity for states on von Neumann algebras generated by the union of (not necessarily commutative) von Neumann subagebras which commute with each other. This study has been already begun in [2] using several a priori different notions of noncommutative markovianity. In this paper we assume to deal with the particular case of states which define odd stochastic couplings (as developed in [3]) for all couples of von Neumann algebras involved. In this situation these definitions are equivalent, and in this case it is possible to get the full noncommutative generalization of the basic classical Markov theory results. In particular we get a correspondence theorem, and an explicit structure theorem for Markov states.},
author = {Cecchini, Carlo},
journal = {Banach Center Publications},
keywords = {Markov state; commuting von Neumann algebras; Tomita theory; generalized conditional mean values; noncommutative Markov chain; modular automorphisms; Markov triple},
language = {eng},
number = {1},
pages = {111-118},
title = {Markovian processes on mutually commuting von Neumann algebras},
url = {http://eudml.org/doc/208830},
volume = {43},
year = {1998},
}

TY - JOUR
AU - Cecchini, Carlo
TI - Markovian processes on mutually commuting von Neumann algebras
JO - Banach Center Publications
PY - 1998
VL - 43
IS - 1
SP - 111
EP - 118
AB - The aim of this paper is to study markovianity for states on von Neumann algebras generated by the union of (not necessarily commutative) von Neumann subagebras which commute with each other. This study has been already begun in [2] using several a priori different notions of noncommutative markovianity. In this paper we assume to deal with the particular case of states which define odd stochastic couplings (as developed in [3]) for all couples of von Neumann algebras involved. In this situation these definitions are equivalent, and in this case it is possible to get the full noncommutative generalization of the basic classical Markov theory results. In particular we get a correspondence theorem, and an explicit structure theorem for Markov states.
LA - eng
KW - Markov state; commuting von Neumann algebras; Tomita theory; generalized conditional mean values; noncommutative Markov chain; modular automorphisms; Markov triple
UR - http://eudml.org/doc/208830
ER -