Preservers of unitary similarity functions on Lie products of matrices

Jianlian Cui Department of Mathematics, Tsinghua University Chi-Kwong Li Department of Mathematics, College of William & Mary, Williamsburg Yiu-Tung Poon cDepartment of Mathematics, Iowa State University, Ames

General Mathematics mathscidoc:1611.13001

Linear Algebra and its Applications, 498, 160-180, 2016.6
Denote by Mnthe set of n ×ncomplex matrices. Let f:Mn→[0, ∞)be a continuous map such that f(μUAU∗) =f(A)for any complex unit μ, A ∈Mnand unitary U∈Mn, f(X) =0if and only if X=0and the induced map t →f(tX)is monotonically increasing on [0, ∞)for any rank onenilpotent X∈Mn. Characterization is given for surjective maps φon Mnsatisfying f(AB−BA) =f(φ(A)φ(B) −φ(B)φ(A)). The general theorem isthen used to deduce results on special cases when the function is the pseudo spectrum and the pseudo spectral radius.
Lie product; Unitary similarity invariant function; Pseudo spectrum
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@inproceedings{jianlian2016preservers,
  title={Preservers of unitary similarity functions on Lie products of matrices},
  author={Jianlian Cui, Chi-Kwong Li, and Yiu-Tung Poon},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161125155320341843641},
  booktitle={Linear Algebra and its Applications},
  volume={498},
  pages={160-180},
  year={2016},
}
Jianlian Cui, Chi-Kwong Li, and Yiu-Tung Poon. Preservers of unitary similarity functions on Lie products of matrices. 2016. Vol. 498. In Linear Algebra and its Applications. pp.160-180. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20161125155320341843641.
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