多项式零点保持线性映射

设H是维数大于2的复Hilbert空间,β(H)代表H上所有有界线性算子全体．假定Φ是从β(H)到其自身的弱连续线性双射．我们证明了映射Φ满足对所有的A,B∈β(H),AB=BA~*蕴涵Φ(A)Φ(B)=Φ(B)Φ(A)~*当且仅当存在非零实数c和酉算子U∈(?)(H),使得Φ(A)=cUAU~*对所有的A∈β(H)成立．     

自伴标准算子代数上强保持k-斜交换性映射的刻画

令H是维数大于2的复Hilbert空间,A是H上自伴标准算子代数.对于给定的正整数k≥1,H上算子A与B的k-斜交换子递推地定义为_*[A,B]_k=_*[A,_*[A,B]_k-1],其中_*[A,B]₀=B,_*[A,B]₁=AB-BA^*.设k≥4,φ是A上的值域包含所有一秩投影的映射.本文证明了φ满足_*[φ（A）,φ（B）]_k=_*[A,B]_k对任意A,B∈A都成立的充分必要条件是φ（A）=A对任意A∈A都成立,或φ（A）=-A对任意A∈A都成立.当k是偶数时后一情形不出现.     

Additive Mappings Preserving Rank-one Idempotents

A complete characterization of additive mappings φ ： B（X）→B（Y）, which map rank-one idempotents to themselves or to zero, is given.     

Maps on the -dimensional subspaces of a Hilbert space preserving principal angles

In a former paper we studied transformations on the set of all -dimensional subspaces of a Hilbert space which preserve the principal angles. In the case when , we could determine the general form of all such maps. The aim of this paper is to complete our result by considering the problem in the remaining case .

     

量子态上保凸组合最大特征值的映射北大核心CSCD

量子态即Hilbert空间上迹为1的正算子.量子态集合是一个凸集本文刻画了量子态集合上保持其凸组合的最大特征值不变的映射.     

Strong 3-commutativity preserving maps on standard operator algebras

Let X be a Banach space of dimension ≥ 2 over the real or complex field F and A a standard operator algebra in B(X). A map Φ :A →A is said to be strong 3-commutativity preserving if [Φ(A), Φ(B)]3 = [A,B]3 for all A,B∈ A, where[A,B]3 is the 3-commutator of A,B defined by[A, B]3 = [[[A, B],B],B] with [A,B] = AB-BA. The main result in this paper is shown that.,if Φ is a surjective map on A, then Φ is strong 3-commutativity preserving if and only if there exist a functional h : A →F and a scalar λ∈ F with λ~4 = 1 such that Φ(A)=λ A+h(A)I for all A ∈ A.