Multi-norms and the injectivity of $L^p(G)$

H. Garth Dales, Matthew Daws, Hung Le Pham +1

Let $G$ be a locally compact group, and take $p\in (1,\infty )$. We prove that the Banach left $L^1(G)$-module $L^p(G)$ is injective (if and) only if the group $G$ is amenable. Our p…