Jacek Krajczok, University of Glasgow
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 approximation the constant function by functions in the Fourier algebra. The notion of amenability was relaxed in various directions: 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 the constant function by functions in the Fourier algebra, but in much weaker sense. During the talk I’ll introduce AP for locally compact quantum groups, discuss some of its permanence properties and relation to w*OAP of quantum group von Neumann algebra. The talk is based on a joint work with Matthew Daws and Christian Voigt.