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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.

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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.

Item Type: Article
Journal or Publication Title: Journal of the London Mathematical Society
Uncontrolled Keywords: injectivity
Subjects: Q Science > QA Mathematics
Departments: Faculty of Science and Technology > Mathematics and Statistics
ID Code: 55805
Deposited By: ep_importer_pure
Deposited On: 10 Jul 2012 08:47
Refereed?: Yes
Published?: Published
Last Modified: 09 Oct 2013 13:14
Identification Number:
URI: http://eprints.lancs.ac.uk/id/eprint/55805

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