Speaker: b>Hikaru Awazu (University of Tokyo)

Title: Amenability of group actions on compact spaces and the associated Banach algebras

Time/Date: 4:45-6:15pm, June 17 (Tue.), 2025

Room: 117 Math. Sci. Building (It will be also online. The Zoom link is the same as before. If you don't have one, please ask Kawahigashi.)

Abstract: For a topological group G , amenability can be characterized by the amenability of the convolution Banach algebra L¹(G). Here a Banach algebra A is called amenable if every bounded derivation from A into any dual-type A-A-Banach bimodule are inner.

We extend this classical result to discrete group actions on compact Hausdorff spaces. By introducing a Banach algebra naturally associated with the action and adopting a suitably weakened notion of amenability for Banach algebras, we obtain an analogous characterization of amenable actions.

As a lemma, we also proved a fixed-point property for amenable actions that strengthens the theorem of Dong and Wang (2015).

This talk is based on the following preprint: A.Hikaru "Amenability of group actions on compact spaces and the associated Banach algebras" arXiv:2504.08357