Chain rules for canonical state extensions on von Neumann algebras
Colloquium Mathematicum, Tome 64 (1993) no. 1, pp. 115-119
In previous papers we introduced and studied the extension of a state defined on a von Neumann subalgebra to the whole of the von Neumann algebra with respect to a given state. This was done by using the standard form of von Neumann algebras. In the case of the existence of a norm one projection from the algebra to the subalgebra preserving the given state our construction is simply equivalent to taking the composition with the norm one projection. In this paper we study couples of von Neumann subalgebras in connection with the state extension. We establish some results on the ω-conditional expectation and give a necessary and sufficient condition for the chain rule of our state extension to be true.
@article{10_4064_cm_64_1_115_119,
author = {Carlo Cecchini and D\'enes Petz},
title = {Chain rules for canonical state extensions on von {Neumann} algebras},
journal = {Colloquium Mathematicum},
pages = {115--119},
year = {1993},
volume = {64},
number = {1},
doi = {10.4064/cm-64-1-115-119},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/cm-64-1-115-119/}
}
TY - JOUR AU - Carlo Cecchini AU - Dénes Petz TI - Chain rules for canonical state extensions on von Neumann algebras JO - Colloquium Mathematicum PY - 1993 SP - 115 EP - 119 VL - 64 IS - 1 UR - http://geodesic.mathdoc.fr/articles/10.4064/cm-64-1-115-119/ DO - 10.4064/cm-64-1-115-119 LA - en ID - 10_4064_cm_64_1_115_119 ER -
%0 Journal Article %A Carlo Cecchini %A Dénes Petz %T Chain rules for canonical state extensions on von Neumann algebras %J Colloquium Mathematicum %D 1993 %P 115-119 %V 64 %N 1 %U http://geodesic.mathdoc.fr/articles/10.4064/cm-64-1-115-119/ %R 10.4064/cm-64-1-115-119 %G en %F 10_4064_cm_64_1_115_119
Carlo Cecchini; Dénes Petz. Chain rules for canonical state extensions on von Neumann algebras. Colloquium Mathematicum, Tome 64 (1993) no. 1, pp. 115-119. doi: 10.4064/cm-64-1-115-119
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