Nonconventional ergodic theorem for quantum "diagonal measures" in non ergodic case

Details Nonconventional ergodic theorem for quantum "diagonal measures" in non ergodic case Nonconventional ergodic theorem for quantum "diagonal measures" in non ergodic case

2012-03-23

arxiv.org/abs/1203.5200v1

Mathematics

Operator Algebras

16 pages

Scientific paper

We extend the nonconventional Furstenberg ergodic theorem for the "diagonal measures", to the non ergodic situation. In order to get the result, we should add a natural algebraic condition which plays a crucial role in the quantum (i.e. non commutative) non ergodic situation. Such a condition is trivial in the classical case, as well as in the quantum ergodic situation provided that the support in the bidual of the state under consideration belongs to the center.

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