A Non-commutative Fejér Theorem for Crossed Products, the Approximation Property, and Applications
A Non-commutative Fejér Theorem for Crossed Products, the Approximation Property, and Applications
Abstract We prove that a locally compact group has the approximation property (AP), introduced by Haagerup–Kraus [ 21], if and only if a non-commutative Fejér theorem holds for its associated $C^*$- or von Neumann crossed products. As applications, we answer three open problems in the literature. Specifically, we show that …