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

作　　者：田茹 张艳芳 

机构地区：[1]太原理工大学数学学院,山西 太原

出　　处：《应用数学进展》2024年第1期244-254,共11页Advances in Applied Mathematics

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。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.

关 键 词：c-数值域 ξ-Lie积 保持问题 

分 类 号：O17[理学—数学]