Characterisations of Pseudo-amenability (Thesis)

We start this thesis by introducing the theory of locally compact groups and their associated Haar measures. We provide examples and prove important results about locally compact and more specifically amenable groups. One such result is known as the Følner condition, which characterises the class amenable groups. We then use this characterisation to define the notion of a pseudo-amenable group. Our central theorem that we present provides new characterisations of pseudo-amenable groups. These characterisations allows us to prove several new results about these groups, which closely mimic well known results about amenable groups. For instance, we show that pseudo-amenability is preserved under closed subgroups and homomorphisms.