Jordan isomorphisms of nest algebras
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- by Fangyan Lu PDF
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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.References
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Additional Information
- Fangyan Lu
- Affiliation: Department of Mathematics, Suzhou University, Suzhou 215006, People’s Republic of China
- Email: fylu@pub.sz.jsinfo.net
- 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
- © Copyright 2002 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 131 (2003), 147-154
- MSC (2000): Primary 47L35, 47L20, 46H10
- DOI: https://doi.org/10.1090/S0002-9939-02-06587-5
- MathSciNet review: 1929034