Operator algebra Seminar by Paul Jolissaint

Relative inner amenability and relative property gamma

We say that a subgroup $H$ of a group $G$ is inner amenable relative to $G$ if it is proper and if its action by conjugation on $G\setminus H$ admits an invariant mean. We will discuss this property and present families of examples. The analoguous relative property gamma for subfactors in type II_1 factors will also be discussed. In particular, it will be compared to D. Bisch's property gamma for an inclusion of type II_1 factors, and a characterization of non-Kazhdan's groups will be given.