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.
2
Dostęp do pełnego tekstu na zewnętrznej witrynie WWW
We generalize a result of Choi and Effros on the range of a contractive completely positive projection in a C*-algebra to the case when this projection is only strongly positive using, moreover, an elementary argument instead of a 2×2-matrix technique.
3
Dostęp do pełnego tekstu na zewnętrznej witrynie WWW