Corollary 1

The space A(G) is dense in $L^1(G)$ and in $L^2(G)$. It is also dense in Stell(G), and its image $\widehat{A}(G)$ under the Fourier transform is dense in $\mathscr{C}_0(\widehat{G})$.

Assertion (iv) of the proposition provides the first assertion. Since $L^1(G)$ is dense in Stell(G), the second follows from it, and the last then follows from Prop. 5 of II, p. 209.