Matthew Wiersma, Department of Pure Mathematics, University of Waterloo
“Lp-Fourier and Fourier-Stieltjes algebras”
Let G be a locally compact group and 1 ≤ p < ∞. A continuous unitary representation π : G → B(H) is an Lp-representation if, roughly speaking, many of the coefficient functions s → 〈π(s)x,x〉 are in Lp(G) for x ∈ H. We investigate the norm-closed and weak*-closed coefficient spaces of the Fourier-Stieltjes algebra arising from the Lp-representations. These are always ideals of the Fourier-Stieltjes algebra containing the Fourier algebra and reflect properties of the underlying group G.