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Jordan isomorphisms of nest algebras

Author: Fangyan Lu
Journal: Proc. Amer. Math. Soc. 131 (2003), 147-154
MSC (2000): Primary 47L35, 47L20, 46H10
Published electronically: May 22, 2002
MathSciNet review: 1929034
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Abstract: Let $\mathcal{T}(N)$ and $\mathcal{T}(\mathcal{M})$ be two nest algebras. A Jordan isomorphism $\phi $ from $\mathcal{T}(N)$ onto $\mathcal{T}(\mathcal{M})$ is a bijective linear map such that $\phi (T^{2})=\phi (T)^{2}$ for every $T\in \mathcal{T}(\mathcal{N})$. In this note, we prove that every Jordan isomorphism of nest algebras is of the form $T\rightarrow STS^{-1}$ or $T\rightarrow ST^{*}S^{-1}$ and then is, in fact, an isomorphism or an anti-isomorphism.

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Additional Information

Fangyan Lu
Affiliation: Department of Mathematics, Suzhou University, Suzhou 215006, People’s Republic of China

Keywords: Jordan isomorphism, nest algebra, nilpotent Jordan ideal
Received by editor(s): June 8, 2000
Received by editor(s) in revised form: October 30, 2000, and August 16, 2001
Published electronically: May 22, 2002
Communicated by: David R. Larson
Article copyright: © Copyright 2002 American Mathematical Society

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