Noncommutative Poincaré recurrence theorem

Andrzej Łuczak
2001 Colloquium Mathematicum  
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
more » ... assification: Primary 46L51; Secondary 28D05. Key words and phrases: Poincaré's recurrence theorem, Jordan morphisms of a von Neumann algebra, faithful weight.
doi:10.4064/cm89-1-1 fatcat:nnyu7avaxna7bj6umq25a7qda4