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## Noncommutative Poincaré recurrence theorem

### Tom 89 / 2001

Colloquium Mathematicum 89 (2001), 1-6 MSC: Primary 46L51; Secondary 28D05. DOI: 10.4064/cm89-1-1

#### Streszczenie

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 $L^\infty$-space rather than the original measure space, thus allowing the replacement of the commutative von Neumann algebra $L^\infty$ by a noncommutative one.

#### Autorzy

• Andrzej ŁuczakFaculty of Mathematics
Łódź University
Stefana Banacha 22
90-238 Łódź Poland
e-mail

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