Characterizations of Jordan Isomorphisms of Nest Algebras

Xiao Hui ZHANG, Jian Hua ZHANG

Acta Mathematica Sinica, Chinese Series ›› 2013, Vol. 56 ›› Issue (4) : 553-560.

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Acta Mathematica Sinica, Chinese Series ›› 2013, Vol. 56 ›› Issue (4) : 553-560. DOI: 10.12386/A2013sxxb0056
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Characterizations of Jordan Isomorphisms of Nest Algebras

  • Xiao Hui ZHANG, Jian Hua ZHANG
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Abstract

Let AlgN and AlgM be non-trivial nest algebras on a complex separable Hilbert space H, and φ: AlgN → AlgM be a unital bijection. In the paper, we prove that if φ satisfies φ(AoB)=φ(A)oφ(B) for any A,B ∈ AlgN with AB=0, then φ is either an isomorphism or an anti-isomorphism.

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nest algebra / Jordan isomorphism / isomorphism

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Xiao Hui ZHANG, Jian Hua ZHANG. Characterizations of Jordan Isomorphisms of Nest Algebras. Acta Mathematica Sinica, Chinese Series, 2013, 56(4): 553-560 https://doi.org/10.12386/A2013sxxb0056

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