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

 

Linear maps on operator algebras that preserve elements annihilated by a polynomial


Authors: Jinchuan Hou and Shengzhao Hou
Journal: Proc. Amer. Math. Soc. 130 (2002), 2383-2395
MSC (2000): Primary 47B48, 47L10, 46L05
Published electronically: February 12, 2002
MathSciNet review: 1897464
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Abstract: In this paper some purely algebraic results are given concerning linear maps on algebras which preserve elements annihilated by a polynomial of degree greater than 1 and with no repeated roots and applied to linear maps on operator algebras such as standard operator algebras, von Neumann algebras and Banach algebras. Several results are obtained that characterize such linear maps in terms of homomorphisms, anti-homomorphisms, or, at least, Jordan homomorphisms.


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Additional Information

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

Shengzhao Hou
Affiliation: Institute of Mathematics, Fudan University, Shanghai, 200433, People’s Republic of China
Email: 970004@fudan.edu.cn

DOI: http://dx.doi.org/10.1090/S0002-9939-02-06362-1
PII: S 0002-9939(02)06362-1
Keywords: Operator algebras, linear preservers, homomorphisms
Received by editor(s): June 23, 2000
Received by editor(s) in revised form: March 23, 2001
Published electronically: February 12, 2002
Additional Notes: The project is partially supported by NNSFC and PNSFS
Communicated by: David R. Larson
Article copyright: © Copyright 2002 American Mathematical Society