|
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== * 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. 抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)』 ■ウィキペディアで「Amenable Banach algebra」の詳細全文を読む スポンサード リンク
|