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C*-代数上强保k-skew交换性的映射
Strong k-skew Commutativity Preserving Maps on C*-algebras
设A是含单位元I的C*-代数，Φ：A→A是满射.本文证明Φ强保k-skew交换性，即*[Φ（A），Φ（B）]k=*[A，B]k，∀A，B∈A当且仅当Φ（A）=Φ（I）A，∀A∈A，其中Φ（I）∈Z（A），Φ（I）*=Φ（I），Φ（I）k+1=I，Z（A）是A的中心.特别地，若Z（A）=CI，则Φ：A→A强保k-skew交换性当且仅当Φ（A）=A，∀A∈A或Φ（A）=-A，∀A∈A.若k是偶数，后一种情形不会出现.
Let A be a C*-algebra with the unit I, Φ:A → A be a surjective map. We show that Φ preserves strong k-skew commutativity, that is, Φ satisfies *[Φ(A), Φ(B)]k=*[A, B]k, ∀ A, B ∈ A if and only if Φ(A)=Φ(I)A, ∀ A ∈ A, where Φ(I) ∈ Z (A) with Φ(I)*=Φ(I) and Φ(I)k+1=I, Z (A) is the center of A. In particular, if Z (A)=CI, then Φ:A → A preservers strong k-skew commutativity if and only if Φ(A)=A, ∀ A ∈ A or Φ(A)=-A, ∀ A ∈ A. The latter case does not occur if k is even.
C*-代数 / k-skew交换子 / 强保k-skew交换性映射 {{custom_keyword}} /
C*-algebras / k-skew commutator / strong k-skew commutativity preserving maps {{custom_keyword}} /
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国家自然科学基金资助项目（11001194）
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