【摘要】 令T是无穷维复Banach空间X上的拟幂零算子，且x∈X{0}.定义■令Λ(T)={k_x:x≠0},称为T的幂集.证明Λ(T)是右闭的，即对Λ(T)的每个非空有界子集σ有sup σ∈Λ(T).特别地，证明对任意无穷维复Banach空间X,存在X上的拟幂零算子T,使得Λ(T)=[0,1].更多还原

【Abstract】 Let T be a quasinilpotent operator on an infinite dimensional complex Banach space X and x∈X{0}. Define■Let Λ(T)={k_x: x≠0}, and call it the power set of T. We prove that Λ(T) is right closed, that is, sup σ∈Λ(T) for each nonempty bounded subset σ of Λ(T). In particular, we prove that for any infinite dimensional complex Banach space X, there exists a quasinilpotent operator T on X such that Λ(T)=[0,1].更多还原