套代数上的零点Lie可导映射

Lie Derivable Mappings at Zero Point on Nest Algebras

设N是维数大于2的复可分Hilbert空间H上的套且r(N)是相应的套代数.本文证明了套代数r(N)上的每一个零点Lie可导映射都具有形式A→AT—TA+λA+h(A)I,其中T∈r(N),λ∈C且h:r(N)→C为一个线性映射.

Let N be a nest on a separable Hilbert space H with dim H 〉 2 and T（N） be the associated nest algebra. We prove that every Lie derivable mapping at zero point from T（N） into itself is of the form A→AT-TA＋λA＋h（A）I, where T∈T（N）,λ∈C and h：T（N）→CI is a linear mapping.