Operators on the Fourier Algebra with Weakly Compact Extensions

Abstract

We let G denote an infinite compact group, and Ĝ its dual. We use the notation of our book [3, Chapters 7 and 8]. Recall that A(G) denotes the Fourier algebra of G (an algebra of continuous functions on G), and denotes its dual space under the pairing 〈f, ϕ〉 , (f ∊ A (G), ϕ ∊ ). Further, note is identified with the C*-algebra of bounded operators on L 2(G) commuting with left translation. The module action of A (G) on is defined by the following: for f ∊ A (G), ϕ ∊ , f · ϕ ∊ by