From Wikipedia, the free encyclopedia
In mathematics, specifically in
functional analysis, 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.
Examples
References
- 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).
- Volker Runde, "Amenable Banach Algebras. A Panorama", Springer Verlag (2020).
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