Multi-norms and the injectivity of Lp(G)
2012
Let G be a locally compact group, and take p∈(1, ∞). 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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