Linear maps preserving ideals of C$^{*}$-algebras
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- by Jianlian Cui and Jinchuan Hou PDF
- Proc. Amer. Math. Soc. 131 (2003), 3441-3446 Request permission
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.References
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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
- 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
- © Copyright 2003 American Mathematical Society
- 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
- MathSciNet review: 1990633