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 | References | Similar Articles | Additional Information

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