广义＊-Lie可导映射

Generalized ~＊-Lie derivable mappings

证明了含单位元C*代数上可加的广义*-Lie导子是一个保*的可加导子。研究了因子von Neumann代数上拟正规可导映射。设H是维数大于2的复可分Hilbert空间,M是作用在H上维数大于1的因子von Neu-mann代数。若Ф:M→M是线性拟正规可导映射,则存在数λ∈R和算子T∈M且T+T*=λI,以及线性映射h:M→CI,使得对任意A∈M,有Ф(A)=AT-TA+h(A),且h([A,A*])=0。

It is shown that generalized ＊-Lie derivable additive mappings on C＊ algebras with unit is an additive preserving ＊-derivation.Quasi normal derivable linear mappings on factor von Neumann algebras is considered.Let M with dim H1 be a factor von Neumann algebra acting on a complex separable Hilbert space H with dim H2.If Ф：M →M is a quasi normal derivable linear mapping,then Ф（A）=AT-TA＋h（A） for all A∈M,where T∈M,h：M→CI is a linear mapping with h（）=0 and T＋T＊=λI,λ∈R.