• Corpus ID: 204800946

Von Neumann equivalence and properly proximal groups

  title={Von Neumann equivalence and properly proximal groups},
  author={Ishan Ishan and Jesse Peterson and Lauren C. Ruth},
  journal={arXiv: Operator Algebras},
We introduce a new equivalence relation on groups, which we call von Neumann equivalence, that is coarser than both measure equivalence and $W^*$-equivalence. We introduce a general procedure for inducing actions in this setting and use this to show that many analytic properties, such as amenability, property (T), and the Haagerup property, are preserved under von Neumann equivalence. We also show that proper proximality, which was defined recently by Boutonnet, Ioana, and the second author… 

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