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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Numerical radius distance-preserving maps on $\mathcal{B}(H)$


Authors: Zhaofang Bai and Jinchuan Hou
Journal: Proc. Amer. Math. Soc. 132 (2004), 1453-1461
MSC (2000): Primary 47H20, 47B49; Secondary 47A12
Published electronically: September 30, 2003
MathSciNet review: 2053353
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Abstract: Let $H$ be a complex Hilbert space, $\mathcal {B}(H)$ be the algebra of all bounded linear operators on $H$, $\mathcal {H}(H)$ be the subset of all selfadjoint operators in $\mathcal {B}(H)$ and $\mathcal{V}=\mathcal{B}(H)$ or $ {\mathcal H}(H)$. Denote by $w(A)$ the numerical radius of $A\in\mathcal{B}(H)$. We characterize surjective maps $\Phi:{\mathcal V}\rightarrow{\mathcal V}$ that satisfy $w(\Phi (A)-\Phi (B))=w(A-B)$ for all $A,B\in{\mathcal V}$ without the linearity assumption.


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Additional Information

Zhaofang Bai
Affiliation: School of Science, Xi$^{′}$an Jiaotong University, Xi$^{′}$an, 710049, P. R. China; Department of Mathematics, Shanxi Teachers University, Linfen, 041004, P. R. China

Jinchuan Hou
Affiliation: Department of Mathematics, Shanxi Teachers University, Linfen, 041004, P. R. China; Department of Mathematics, Shanxi University, Taiyuan, 030000, P. R. China
Email: jhou@dns.sxtu.edu.cn

DOI: http://dx.doi.org/10.1090/S0002-9939-03-07190-9
PII: S 0002-9939(03)07190-9
Keywords: Numerical radius, Isometry, C*-isomorphism
Received by editor(s): September 27, 2002
Received by editor(s) in revised form: January 11, 2003
Published electronically: September 30, 2003
Additional Notes: This work was supported partially by NNSFC and PNSFS
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2003 American Mathematical Society