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Jordan isomorphisms of nest algebras
Authors:Fangyan Lu
Institution:Department of Mathematics, Suzhou University, Suzhou 215006, People's Republic of China
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.

Keywords:Jordan isomorphism  nest algebra  nilpotent Jordan ideal
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