【摘要】 令N是Hilbert空间H上的非平凡完备套.若线性映射φ={φ^（n）}_n∈N满足对任意n∈N以及S,T∈alg N,且ST=G,φ^（n）（sT）=∑_i+j=nφ^（i）（S）φ^（j）（T）,则称φ为alg N上的G点高阶可导映射.若G点高阶可导映射φ={φ^（n）)}_n∈N为高阶导子,则称G为alg N上的高阶全可导点.本文证明了,G∈alg N为高阶全可导点当且仅当G≠0.更多还原

【Abstract】 Let N be a nontrivial complete nest on a Hilbert space H.We say that φ ={φ^（n）}_n∈N is a higher derivable Unear mapping at G if φ（ST）= ∑_i+j=nφ^（i）（S）φ^（j）（T）for all n ∈ N and S,T ∈ alg N with ST = G.An element G ∈ alg N is called a higher all-derivable point of alg N if every higher derivable Unear mapping φ = {φ^（n）}_n∈N at G is a higher derivation.In this paper,we show G G alg N is a higher all-derivable point if and only if G≠ 0.更多还原