Amenable Banach algebra

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A Banach algebra, A, is amenable if all bounded derivations from A into dual Banach A-bimodules are inner (that is of the form for some in the dual module).

An equivalent characterization is that A is amenable if and only if it has a virtual diagonal.



  • 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).