算子代数上保持ξ-Lie积的c-数值域的映射
Maps Preserving the c-Numerical Range of ξ-Lie Product on Operator Algebras
DOI: 10.12677/AAM.2024.131027, PDF,   
作者: 田 茹, 张艳芳*：太原理工大学数学学院，山西 太原
关键词: c-数值域；ξ-Lie积；保持问题；c-Numerical Range； ξ-Lie Product； Preserving Problems
摘要: 令B(H)是复Hilbert空间H上有界线性算子全体组成的代数，对于，Wc(A)表示算子A∈B(H)的c-数值域。本文主要研究了在H是有限维的情形下，B(H)上一类映射保持算子ξ-Lie积的数值域的刻画。具体说来，若且c满足一定条件时，若是满射，满足对任意的A,B∈B(H)成立，当且仅当存在H上的酉算子U以及常数使得对所有T∈B(H)成立。
Abstract: Let B(H) be the algebra of all bounded linear operators on an complex Hilbert space H. For , Wc(A) denotes the c-numerical range of an operator A in B(H) . In this paper, we consider maps on B(H) prserving the c-numerical range of ξ-Lie Product. When the dimension of H is finite and belongs to a certain kind, it is shown that is surjective maps satisfying for any A,B∈B(H) , if and only if there exist a unitary operator U on H such that holds for all T∈B(H) , where is a scalar.
文章引用：田茹, 张艳芳. 算子代数上保持ξ-Lie积的c-数值域的映射[J]. 应用数学进展, 2024, 13(1): 244-254. https://doi.org/10.12677/AAM.2024.131027

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