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

DOI:
https://doi.org/10.1090/S0002-9939-02-06362-1

Published electronically:
February 12, 2002

MathSciNet review:
1897464

Full-text PDF

Abstract | References | Similar Articles | Additional Information

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:
https://doi.org/10.1090/S0002-9939-02-06362-1

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