PRESERVERS OF UNITARY SIMILARITY FUNCTIONS ON LIE PRODUCTS OF MATRICES
PRESERVERS OF UNITARY SIMILARITY FUNCTIONS ON LIE PRODUCTS OF MATRICES
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DOI：
10.1016/j.laa.2015.02.036
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发表时间：
2014-10
影响因子：
1.1
通讯作者：
Jianlian Cui;Chi-Kwong Li;Y. Poon
中科院分区：
文献类型：
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作者：
Jianlian Cui;Chi-Kwong Li;Y. Poon
用n表示n× n个复矩阵的集合。让f: M n→[0,∞)是一个连续的地图,这样(μU U⁎)= f (a)对任何复杂的单位μ,∈M n和酉U∈M n, f (X) = 0当且仅当X = 0和诱导映射f t↦X (t)是单调递增在[0,∞)任何排名一个幂零X∈M n。描述了对满射地图ϕmn满意(−B) = f(ϕϕ(a) (B)−ϕ(B)ϕ(a))。然后利用一般定理推导出函数为伪谱和伪谱半径时的特殊情况的结果。
Denote by M n the set of n× n complex matrices. Let f: M n→[0,∞) be a continuous map such that f (μ U A U⁎)= f (A) for any complex unit μ, A∈ M n and unitary U∈ M n, f (X)= 0 if and only if X= 0 and the induced map t↦ f (t X) is monotonically increasing on [0,∞) for any rank one nilpotent X∈ M n. Characterization is given for surjective maps ϕ on M n satisfying f (A B− B A)= f (ϕ (A) ϕ (B)− ϕ (B) ϕ (A)). The general theorem is then used to deduce results on special cases when the function is the pseudo spectrum and the pseudo spectral radius.