设H为复Hilbert空间, Sa(H)代表H上的有界自伴算子组成的空间, Φ:Sa(H)→Sa(H)是满射且复数ξ,η ∈ C\{1}, 则Φ满足 W(AB-ξBA)=W(Φ(A)Φ(B)-ηΦ(B)Φ(A))对所有A,B ∈ Sa(H)成立当且仅当存在酉算子或者共轭酉算子U,使得Φ(A)=UAU*对所有A ∈ Sa(H)成立,或者 Φ(A)=-UAU*对所有A ∈ Sa(H)成立.
Abstract
Let H be a complex Hilbert space and Sa(H) the space of all self adjoint operators on H. Φ : Sa(H) → Sa(H) is a surjective map. For ξ, η ∈ C\ {1}, then Φ satisfies that W(AB - ξBA) = W(Φ(A)Φ(B) - ηΦ(B)Φ(A)) for all A,B ∈ Sa(H) if and only if there exists a unitary operator or con-unitary operator U such that Φ(A) = UAU* for all A ∈ Sa(H) or Φ(A) = -UAU* for all A ∈ Sa(H).
关键词
数值域 /
保持映射 /
因子乘积
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Key words
Numerical range /
preservers /
product up to a factor
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参考文献
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