在vN代数的可逆元处可导映射的特征

M是一个无限维复Hilbert空间H上的vN代数，ψ为M上一个线性映射，Z∈M，称ψ在Z处可导，如果ψ满足ψ（ST）=ψ（S）T＋Sψ（T）对任意S，T∈M并且ST=Z成立。现令Z∈M是一个可逆元，本文证明了若M上范数连续的映射ψ在Z处可导，则ψ在M的单位元I处可导，从而可得ψ是M的一个内导子。

Characteristics of Derivable Mapping at an Invertible Element on vN Algebra

Let M be a vN algebra on an infinite-dimensional complex Hilbert space H.Z∈M,Ψ is a derivable mapping at Z only if Ψ is a linear mapping and Ψ(ST)=Ψ(S)T+SΨ(T) for any S,T∈M with ST=Z.Now let Z∈M be an invertible element,in this paper the result that Ψ is a derivable mapping at I which is the unit of M,so Ψ is an inner derivation,is proved provided that Ψ is a norm-continuous derivable mapping at Z on M.