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arXiv · 1101.4320

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

H. Garth Dales·Matthew Daws·Hung Le Pham·Paul Ramsden
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Abstract

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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BibTeXRIS

H. Garth Dales, Matthew Daws, Hung Le Pham, Paul Ramsden. 2011-01-22. Multi-norms and the injectivity of $L^p(G)$. https://arxiv.org/abs/1101.4320

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