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Non-commutative Pointwise Ergodic Theorem for Actions of Amenable Groups

By Léonard Cadilhac

Appears in collection : Arbre de Noël du GDR « Géométrie non-commutative »

Birkhoff's famous theorem asserts the pointwise convergence of ergodic averages associated with a measure preserving transformation of a measure space. In this talk, I will discuss generalizations of this theorem in two directions: the transformation will be replaced by the action of an amenable group, and the measure space by a von Neumann algebra equipped with a trace. A central role will be played by the notion of non-commutative maximal function, which extends for our purposes the notion of supremum to families of operators. The talk is based on joint work with Simeng Wang.

Information about the video

  • Date of recording 12/1/22
  • Date of publication 12/4/22
  • Institution IHES
  • Language English
  • Audience Researchers
  • Format MP4

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