Noncommutative Poincaré recurrence theorem

Andrzej Łuczak. "Noncommutative Poincaré recurrence theorem." Colloquium Mathematicae 89.1 (2001): 1-6. <http://eudml.org/doc/283634>.

@article{AndrzejŁuczak2001,
abstract = {Poincaré’s classical recurrence theorem is generalised to the noncommutative setup where a measure space with a measure-preserving transformation is replaced by a von Neumann algebra with a weight and a Jordan morphism leaving the weight invariant. This is done by a suitable reformulation of the theorem in the language of $L^\{∞\}$-space rather than the original measure space, thus allowing the replacement of the commutative von Neumann algebra $L^\{∞\}$ by a noncommutative one.},
author = {Andrzej Łuczak},
journal = {Colloquium Mathematicae},
keywords = {Poincaré’s recurrence theorem; Jordan morphisms of a von Neumann algebra; faithful weight; measure-preserving transformation},
language = {eng},
number = {1},
pages = {1-6},
title = {Noncommutative Poincaré recurrence theorem},
url = {http://eudml.org/doc/283634},
volume = {89},
year = {2001},
}

TY - JOUR
AU - Andrzej Łuczak
TI - Noncommutative Poincaré recurrence theorem
JO - Colloquium Mathematicae
PY - 2001
VL - 89
IS - 1
SP - 1
EP - 6
AB - Poincaré’s classical recurrence theorem is generalised to the noncommutative setup where a measure space with a measure-preserving transformation is replaced by a von Neumann algebra with a weight and a Jordan morphism leaving the weight invariant. This is done by a suitable reformulation of the theorem in the language of $L^{∞}$-space rather than the original measure space, thus allowing the replacement of the commutative von Neumann algebra $L^{∞}$ by a noncommutative one.
LA - eng
KW - Poincaré’s recurrence theorem; Jordan morphisms of a von Neumann algebra; faithful weight; measure-preserving transformation
UR - http://eudml.org/doc/283634
ER -