Amenability and the structure of the algebras 𝐴_{𝑝}(𝐺)

Forrest, Brian

doi:10.1090/S0002-9947-1994-1181182-5

Amenability and the structure of the algebras $A_ p(G)$
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by Brian Forrest

Trans. Amer. Math. Soc. 343 (1994), 233-243

DOI: https://doi.org/10.1090/S0002-9947-1994-1181182-5

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Abstract:

A number of characterizations are given of the class of amenable locally compact groups in terms of the ideal structure of the algebras ${A_p}(G)$. An almost connected group is amenable if and only if for some $1 < p < \infty$ and some closed ideal I of ${A_p}(G)$, I has a bounded approximate identity. Furthermore, G is amenable if and only if every derivation of ${A_p}(G)$ into a Banach ${A_p}(G)$-bimodule is continuous.

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