On linear maps preserving complex symmetry

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:468

Article

Ji, Youqing¹  Liu, Ting²  Zhu, Sen¹ 

[1] Jilin Univ, Dept Math, Changchun 130012, Jilin, Peoples R China

[2] Jilin Univ, Inst Math, Changchun 130012, Jilin, Peoples R China

关键词: Complex symmetric operator;    Linear preserver;    Similarity;    Completely positive map;   

DOI  :  10.1016/j.jmaa.2018.09.004

来源: Elsevier

【 摘 要 】

An operator T on a complex Hilbert space H is said to be complex symmetric if there exists a conjugate-linear, isometric involution C : H -> H so that CTC = T*. This paper is devoted to describing which linear maps leave the class of complex symmetric operators invariant. Complete characterizations are obtained for several classes of linear maps, including similarity transformations, surjective linear isometries, multiplication operators and certain completely positive maps. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free