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Linear maps preserving ideals of C$^{*}$-algebras


Authors: Jianlian Cui and Jinchuan Hou
Journal: Proc. Amer. Math. Soc. 131 (2003), 3441-3446
MSC (2000): Primary 47B48, 47L30, 47A10
DOI: https://doi.org/10.1090/S0002-9939-03-06903-X
Published electronically: February 6, 2003
MathSciNet review: 1990633
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Abstract: We show that every unital linear bijection which preserves the maximal left ideals from a semi-simple Banach algebra onto a C$^{*}$-algebra of real rank zero is a Jordan isomorphism. Furthermore, every unital self-adjoint linear bijection on a countably decomposable factor von Neumann algebra is maximal left ideal preserving if and only if it is a *-automorphism.


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Additional Information

Jianlian Cui
Affiliation: School of Mathematical Sciences, Peking University, Beijing 100871, People’s Republic of China
Address at time of publication: Department of Applied Mathematics, Taiyuan University of Technology, Taiyuan 030024, People’s Republic of China; Department of Mathematics, Shanxi Teachers University, Linfen, 041004, People’s Republic of China
Email: cuijl@dns.sxtu.edu.cn

Jinchuan Hou
Affiliation: Department of Mathematics, Shanxi Teachers University, Linfen, 041004, People’s Republic of China
Email: jhou@dns.sxtu.edu.cn

DOI: https://doi.org/10.1090/S0002-9939-03-06903-X
Keywords: Jordan homomorphism, maximal left ideals, Banach algebras, C$^{*}$-algebras
Received by editor(s): November 7, 2001
Received by editor(s) in revised form: May 27, 2002
Published electronically: February 6, 2003
Additional Notes: This work was supported by NNSFC and PNSFS
Communicated by: Joseph A. Ball
Article copyright: © Copyright 2003 American Mathematical Society

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