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Linear maps on operator algebras that preserve elements annihilated by a polynomial
Author(s):
Jinchuan
Hou;
Shengzhao
Hou
Journal:
Proc. Amer. Math. Soc.
130
(2002),
2383-2395.
MSC (2000):
Primary 47B48, 47L10, 46L05
Posted:
February 12, 2002
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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:
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
Posted:
February 12, 2002
Additional Notes:
The project is partially supported by NNSFC and PNSFS
Communicated by:
David R. Larson
Copyright of article:
Copyright
2002,
American Mathematical Society
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