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Amenable Banach algebra : ウィキペディア英語版
Amenable Banach algebra
A Banach algebra, ''A'', is amenable if all bounded derivations from ''A'' into dual Banach ''A''-bimodules are inner (that is of the form a\mapsto a.x-x.a for some x in the dual module).
An equivalent characterization is that ''A'' is amenable if and only if it has a virtual diagonal.
==Examples==

* If ''A'' is a group algebra L^1(G) 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 \theta from ''A'' to another Banach algebra, then the closure of \overline is amenable.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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