Multi‐norms and the injectivity of Lp(G)

Multi‐norms and the injectivity of Lp(G)

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.

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Veröffentlicht in:Journal of the London Mathematical Society 2012-12, Vol.86 (3), p.779-809
Hauptverfasser: Dales, H. G., Daws, M., Pham, H. L., Ramsden, P.
Format: Artikel
Sprache:eng
Schlagworte:
Mathematical analysis
Proving
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Zusammenfassung: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.
ISSN:0024-6107
1469-7750
DOI:10.1112/jlms/jds026