Von Neumann equivalence and 𝑀_{𝑑} type approximation properties

Abstract

We show that M d M_d -approximation-property, M d M_d -weak-amenability, and M d M_d -weak-Haagerup-property are stable under von Neumann equivalence (hence also Measure equivalence and W*-equivalence). We also show that these properties are inherited from lattices.