Maps preserving numerical radius distance on ${\rm C}^*$-algebras

Tom 162 / 2004

Zhaofang Bai, Jinchuan Hou, Zongben Xu Studia Mathematica 162 (2004), 97-104 MSC: Primary 47B49, 47A12; Secondary 47H20. DOI: 10.4064/sm162-2-1

Streszczenie

We characterize surjective nonlinear maps ${\mit \Phi } $ between unital C*-algebras ${\mathcal A}$ and ${\mathcal B}$ that satisfy $w({\mit \Phi } (A)-{\mit \Phi } (B))=w(A-B)$ for all $A,B\in {\mathcal A}$ under a mild condition that ${\mit \Phi } (I)-{\mit \Phi } (0)$ belongs to the center of ${\mathcal B}$, where $w(A)$ is the numerical radius of $A$ and $I$ is the unit of ${\mathcal A}$.

Autorzy

  • Zhaofang BaiSchool of Science
    Xi'an Jiaotong University
    Xi'an, 710049, P.R. China
    and
    Department of Mathematics
    Shanxi Teachers University
    Linfen, 041004, P.R. China.
  • Jinchuan HouDepartment of Mathematics
    Shanxi University
    Taiyuan, 030000, P.R. China
    e-mail
  • Zongben XuSchool of Science
    Xi'an Jiaotong University
    Xi'an, 710049, P.R. China

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