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Jordan isomorphisms and maps preserving spectra of certain operator products

JC Hou Chi-Kwong Li Ngai-Ching Wong

Functional Analysis mathscidoc:1910.43631

Studia Math, 184, (1), 31-47, 2008.1
Let A1, A2 be (not necessarily unital or closed) standard operator algebras on locally convex spaces X1, X2, respectively. For k 2, define different kinds of products T1 Tk on elements in Ai, which covers the usual product T1 Tk= T1 Tk, and the Jordan triple product T1 T2= T2T1T2. Let : A1 A2 be a (not necessarily linear) map satisfying that ( (A1) (Ak))= (A1 Ak) whenever any one of Ais is of rank zero or one. It is shown that if the range of contains all rank one and rank two operators then it must be a Jordan isomorphism multiplied by a root of unity. Similar results for self-adjoint operators acting on Hilbert spaces are obtained.
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@inproceedings{jc2008jordan,
  title={Jordan isomorphisms and maps preserving spectra of certain operator products},
  author={JC Hou, Chi-Kwong Li, and Ngai-Ching Wong},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020204843466876160},
  booktitle={Studia Math},
  volume={184},
  number={1},
  pages={31-47},
  year={2008},
}
JC Hou, Chi-Kwong Li, and Ngai-Ching Wong. Jordan isomorphisms and maps preserving spectra of certain operator products. 2008. Vol. 184. In Studia Math. pp.31-47. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191020204843466876160.
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