I am looking for books presenting the noncommutative version of ergodic theorems.

The only book I have found is Krengel, Ergodic Theorems, 1985.

Are there other references other than Krengel's book ?

  • 1
    $\begingroup$ What do you mean by "noncommutative ergodic theorems"? Do you want theorems of noncommutative groups acting on measure spaces or of actions on von Neumann algebras? $\endgroup$ – Adrián González-Pérez May 27 '19 at 11:09
  • $\begingroup$ @AdriánGonzález-Pérez the second option, actions on von Neumann algebras. $\endgroup$ – Neil hawking May 27 '19 at 17:37

This is a sufficiently advanced topic so I do not think there is much in book form yet. You can look up

Although I suspect that both are a little bit outdated. You can also look at

which is quite good and has a chapter on noncommutative theory, but it is focused on strong limit theorems, not in Ergodic ones. Nevertheless the language and technicalities are shared.

Apart from that, you would have to look at articles. The usual references for the weak $(1,1)$-inequality of the ergodic maximal are:

The $L_p$ case as well as the real interpolation of maximal inequalities is covered in


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