Title:Topologies, idempotents and ideals
Speaker: Nico Spronk, Waterloo University
Abstract: A classical theorem due to Jacobs, and de Leeuw and Glicksberg, shows that a continuous representation of a topological group G on a reflexive Banach space may be decomposed into a “returning” subspace and a “weakly mixing” subspace. Furthermore, following Dye, Bergelson and Rosenblatt characterized the weakly mixing vectors as those for which the closure of the weak orbit of the vector contains zero. I wish to exhibit a generalization of these results, inspired, in part, by some work of Ruppert on abelian groups. I will exhibit a bijective correspondence between
– central idempotents in the weakly almost periodic compactification of G,
– certain topologies on G, and
– certain ideals in the algebra of weakly almost periodic functions.
Given time, I will indicate some applications to Fourier-Stieltjes algebras.
Time: 13 July, 8:30-9:30, Place: 522 Gewu Building
