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

Dales, H. Garth and Daws, M. and Pham, H. L. and Ramsden, P. (2012) Multi-norms and injectivity of L^p(G). Journal of the London Mathematical Society, 86 (3). pp. 779-809. ISSN 0024-6107

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.