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保持算子截断的可加映射
引用本文:姚洁,吉国兴.保持算子截断的可加映射[J].数学研究及应用,2022,42(1):89-94.
作者姓名:姚洁  吉国兴
作者单位:陕西师范大学数学与统计学院, 陕西 西安 710119
基金项目:国家自然科学基金(Grant No.11771261).
摘    要:Let H be a complex Hilbert space and B(H)the algebra of all bounded linear operators on H.An operator A is called the truncation of B in B(H)if A=PABPA*,where PA and PA*denote projections onto the closures of R(A)and R(A*),respectively.In this paper,we determine the structures of all additive surjective maps on B(H)preserving the truncation of operators in both directions.

关 键 词:truncation  of  operator  operator  equation  additive  map  PRESERVER
收稿时间:2020/9/24 0:00:00
修稿时间:2021/4/27 0:00:00

Additive Maps Preserving the Truncation of Operators
Jie YAO,Guoxing JI.Additive Maps Preserving the Truncation of Operators[J].Journal of Mathematical Research with Applications,2022,42(1):89-94.
Authors:Jie YAO  Guoxing JI
Institution:School of Mathematics and Statistics, Shaanxi Normal University, Shaanxi 710119, P. R. China
Abstract:Let $\mathcal{H}$ be a complex Hilbert space and $\mathcal{B}(\mathcal{H})$ the algebra of all bounded linear operators on $\mathcal{H}$. An operator $A$ is called the truncation of $B$ in $\mathcal B(\mathcal H)$ if $A=P_{A}BP_{A^*}$, where $P_{A}$ and $P_{A^*}$ denote projections onto the closures of $R(A)$ and $R(A^*)$, respectively. In this paper, we determine the structures of all additive surjective maps on $\mathcal{B}(\mathcal{H})$ preserving the truncation of operators in both directions.
Keywords:truncation of operator  operator equation  additive  map    preserver
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