Topological centres for group actions
Speaker:
Jan Pachl
Date and Time:
Friday, December 1, 2017 - 1:30pm to 3:00pm
Location:
Fields Institute, Room 210
Abstract:
Based on joint work with Matthias Neufang and Juris Steprans. By a variant of Foreman's 1994 construction, every tower ultrafilter on ω is the unique invariant mean for an amenable subgroup of S∞, the infinite symmetric group. From this we prove that in any model of ZFC with tower ultrafilters there is an element of ℓ1(S∞)∗∗∖ℓ1(S∞) whose action on ℓ1(ω)∗∗ is w* continuous. On the other hand, in ZFC there are always such elements whose action is not w* continuous.