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

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<mark>Journal publication date</mark>2012
<mark>Journal</mark>Journal of the London Mathematical Society
Issue number3
Volume86
Number of pages31
Pages (from-to)779-809
<mark>State</mark>Published
Early online date25/07/12
<mark>Original language</mark>English

Abstract

Let G be a locally compact group, and take p∈(1, ∞). We prove that the Banach left L1(G)-module Lp(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.