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Let $G$ be a discrete commutative group. Let $p \in [1,\infty)$ and consider the left regular representation $\lambda : \ell^1(G) \to \mathcal{B}(\ell^p(G))$; that is $\lambda(x)y := x*y$, where $$ (x*...

Let $G$ be a locally compact group, let $A(G)$ be the Fourier algebra of $G$. We think of $A(G)$ as a subalgebra of $C_0(G)$. Question 1: Let $f\in A(G)$ be a function that is pointwise positive. ...