Uniqueness of the topology on L<sup>1</sup>(G)
Uniqueness of the topology on L<sup>1</sup>(G)
Let $G$ be a locally compact abelian group and let $X$ be a translation invariant linear subspace of $L^1(G)$. If $G$ is noncompact, then there is at most one Banach space topology on $X$ that makes translations on $X$ continuous. In fact, the Banach spac