Functional Analysis and Applications Seminar 

21/05/2010, 14:00 — 15:00 — Room P3.10, Mathematics Building
Yemon Choi, Université Laval, Québec, Canada

Group representations where all convolution operators have empty residual spectrum

Continuous, bounded representations of a group on a Banach space give rise, via integration, to convolution operators on that space. It turns out that for several natural representations and a large class of groups, any such convolution operator will have empty residual spectrum. In this talk, I shall present some of the background to these questions, and then discuss some recent work on this theme, focusing mainly on the case of discrete groups. The root of all these results is an old observation of Kaplansky, concerning left-invertible elements of the group von Neumann algebra.