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

H. Garth Dales; Matthew Daws; Hung Le Pham; Paul Ramsden

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

Functional Analysis 2012-02-28 v2

Authors: H. Garth Dales , Matthew Daws , Hung Le Pham , Paul Ramsden

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.

Keywords

multi-norms injective module Lp(G) amenable group locally compact group

Cite

@article{arxiv.1101.4320,
  title  = {Multi-norms and the injectivity of $L^p(G)$},
  author = {H. Garth Dales and Matthew Daws and Hung Le Pham and Paul Ramsden},
  journal= {arXiv preprint arXiv:1101.4320},
  year   = {2012}
}

Comments

31 pages; minor typographical and mathematical corrections

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

Abstract

Keywords

Cite

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