Amenable Banach algebra
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An equivalent characterization is that A is amenable if and only if it has a virtual diagonal.
- If A is a group algebra for some locally compact group G then A is amenable if and only if G is amenable.
- If A is a C*-algebra then A is amenable if and only if it is nuclear.
- If A is a uniform algebra on a compact Hausdorff space then A is amenable if and only if it is trivial (i.e. the algebra C(X) of all continuous complex functions on X).
- If A is amenable and there is a continuous algebra homomorphism from A to another Banach algebra, then the closure of is amenable.
- F.F. Bonsall, J. Duncan, "Complete normed algebras", Springer-Verlag (1973).
- H.G. Dales, "Banach algebras and automatic continuity", Oxford University Press (2001).
- B.E. Johnson, "Cohomology in Banach algebras", Memoirs of the AMS 127 (1972).
- J.-P. Pier, "Amenable Banach algebras", Longman Scientific and Technical (1988).
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