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Linear maps preserving ideals of C -algebras
Author(s):
Jianlian
Cui;
Jinchuan
Hou
Journal:
Proc. Amer. Math. Soc.
131
(2003),
3441-3446.
MSC (2000):
Primary 47B48, 47L30, 47A10
Posted:
February 6, 2003
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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:
10.1090/S0002-9939-03-06903-X
PII:
S 0002-9939(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
Posted:
February 6, 2003
Additional Notes:
This work was supported by NNSFC and PNSFS
Communicated by:
Joseph A. Ball
Copyright of article:
Copyright
2003,
American Mathematical Society
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