【摘要】 为了深入研究导子的问题,利用类比的方式给出广义反导子的定义,并研究广义反导子和反导子之间的关系.最后利用零积的性质对它进行刻画.结论是设A是一个Banach代数具有性质(C),且有有界的近似单位元,X是一个Banach A-双模满足{x∈X:axb=0,a,b∈Z(A)}={0}.δ是A到X的一个连续的线性算子满足a,b,c∈A,ab=bc=0■c.δ(b).a=0,则δ是一个广义反导子.更多还原

【Abstract】 In order to further study of derivation,this paper introduces generalized antiderivation definition using the analogy method,and then it gives the relationship between generalized antiderivation and antiderivation.Finaly,it characterizes the generalized antiderivation though zero product properties.The conclusion is that let A be a Banach algebra with the property(C) and having a bounded approximate identity,let X be Banach A-bimodule such that {x∈X:axb=0,a,b∈Z(A)}={0},and let δ:A→X be a continuous linear operator satisfying a,b,c∈A,ab=bc=0■c·δ(b)·a=0,then δ is a generalized derivation.更多还原