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Noncommutative Poincaré recurrence theorem
2001
Colloquium Mathematicum
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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. 2000 Mathematics Subject
doi:10.4064/cm89-1-1
fatcat:nnyu7avaxna7bj6umq25a7qda4