B(X)上保持约当积的固定点的满射  

Surjections on B(X) Preserving the Fixed Points of Jordan Products of Operators in B(X)

作　　者：宋显花 SONG Xian-hua(College of Mathematics and Statistics,Qinghai Normal University,Xining 810008,China)

机构地区：[1]青海师范大学数学与统计学院,青海西宁810008

出　　处：《数学的实践与认识》2021年第3期182-185,共4页Mathematics in Practice and Theory

基　　金：青海师范大学校级项目:线性算子的广义逆研究(2018zr004)。

摘　　要：设B(X)是维数大于等于3的复Banach空间X上有界线性算子全体构成的代数.设A∈B(X),若Ax=x,则称x∈X是算子A的固定点.Fix(A)表示A的所有固定点的集合.本文刻画了B(X)上保持算子的Jordan积的固定点的满射.Let B(X) be the algebra of all bounded linear operators on complex Banach space X with dimX≥3.For any A E B(X),we call x ∈ X a fixed point of A if Ax=x.We denote Fix(A)={x∈X:Ax=x}.In this paper,a characterization is given for surjections on B(X) which preserve the fixed points of Jordan products of operators.

关 键 词：算子代数 保持 固定点 Jordan积 

分 类 号：O177[理学—数学]