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

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

2011-01-22

arxiv.org/abs/1101.4320v2

Mathematics

Functional Analysis

31 pages; minor typographical and mathematical corrections

Scientific paper

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 proof uses the notion of multi-norms. We also
develop the theory of multi-normed spaces.

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