Corollary 1

Every character of $L^1(G)$ is hermitian. The canonical mapping from $\mathsf{X}$(Stell(G)) (Definition 9 of I, p. 125) into $\mathsf{X}(L^1(G))$ is a homeomorphism.

The first assertion follows from Proposition 1 and Lemma 1 by restriction to $L^1(G)$. The second follows from the first and from the corollary of Proposition 20 of I, p. 124.