APPROXIMATION PROPERTIES FOR LOCALLY COMPACT QUANTUM GROUPS

One of the most widely studied properties of groups is the notion of amenability. In one of its many formulations, it gives us a way of approximating constant functions by functions in the Fourier algebra. The notion of amenability was relaxed in various directions. For instance, a very weak form of amenability, called the approximation property (AP), was introduced by Haagerup and Kraus in 1994. It still gives us a way of approximating constant functions by functions in the Fourier algebra, but in a much weaker sense. During the talk, I will introduce AP for locally compact quantum groups, and discuss some of its permanence properties and its relation to the weak* operator approximation property of quantum-group von Neumann algebras. The talk is based on a joint work with Matthew Daws and Christian Voigt.