%0 Journal Article
%T 算子代数上保持ξ-Lie积的c-数值域的映射<br>Maps Preserving the c-Numerical Range of ξ-Lie Product on Operator Algebras
%A 田茹
%A 张艳芳
%J Advances in Applied Mathematics
%P 244-254
%@ 2324-8009
%D 2024
%I Hans Publishing
%R 10.12677/AAM.2024.131027
%X 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<img src=\"Edit_f3cfbee3-5437-447b-a62c-171d7c1e13bc.png\" alt=\"\" />，W<sub>c</sub>(A)表示算子A∈<span>B(H)</span>的c-数值域。本文主要研究了在H是有限维的情形下，<span>B(H)</span>上一类映射保持算子ξ-Lie积的数值域的刻画。具体说来，若<img src=\"Edit_424e63ec-3dc0-46b9-af1f-d32fc85d57d1.png\" alt=\"\" />且c满足一定条件时，若<img src=\"Edit_c1f09ac4-2319-49cc-878f-a4915044d7e1.png\" alt=\"\" />是满射，满足<img src=\"Edit_73b2519e-8517-4169-9067-959bf2d843ae.png\" alt=\"\" />对任意的<span>A,B∈</span><span>B(H)</span>成立，当且仅当存在H上的酉算子U以及常数<img src=\"Edit_da009416-ec53-4897-aae7-369313a12dae.png\" alt=\"\" />使得<img src=\"Edit_7b58a7be-f8e3-42f8-8395-a577de1cfb1d.png\" alt=\"\" />对所有T<span>∈</span><span>B(H)</span>成立。<br />
Let <span>B(H)</span> be the algebra of all bounded linear operators on an complex Hilbert space H. For <img src=\"Edit_b40b0427-8b75-4285-8cae-e34b24929d1e.png\" alt=\"\" />, <span>W</span><sub>c</sub><span>(A)</span> denotes the c-numerical range of an operator A in <span>B(H)</span> . In this paper, we consider maps on <span>B(H)</span> prserving the c-numerical range of ξ-Lie Product. When the dimension of H is finite and <img src=\"Edit_828309e5-d777-400a-ab89-476d4ccd5f54.png\" alt=\"\" /> belongs to a certain kind, it is shown that <img src=\"Edit_da3edc62-6745-43a0-a30f-b7e1bf9c8e32.png\" alt=\"\" /> is surjective maps satisfying <img src=\"Edit_bd79550e-9985-4bd2-9e5f-a087b5b8babd.png\" alt=\"\" /> for any <span>A,B∈</span><span>B(H)</span> , <img src=\"Edit_3cecae13-9d2e-42dc-b20e-7cf262db7f39.png\" alt=\"\" /> if and only if there exist a unitary operator U on H such that <img src=\"Edit_6613306f-80d0-4eb4-aa20-ecbc8669e2cd.png\" alt=\"\" /> holds for all <span>T</span><span>∈</span><span>B(H)</span> , where <img src=\"Edit_b2ea0272-94b6-4101-8a1b-e0668b0b4ea6.png\" alt=\"\" /> is a scalar.
%K c-数值域，ξ-Lie积，保持问题<br>c-Numerical Range
%K ξ-Lie Product
%K Preserving Problems
%U http://www.hanspub.org/journal/PaperInformation.aspx?PaperID=79637