零点处的约当可导映射

2010 International Conference on Computational Intelligence and Software Engineering Pub Date : 2010-12-30 DOI:10.1109/CISE.2010.5677101

Hong-xia Li

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引用次数: 0

摘要

设β是任意因子von Neumann代数M中的任意非平凡巢;φ: algMβ→M为弱连续线性映射。当φ(AB + BA) = φ(a)B + a φ(B) +φ(B) a + Bφ(B) a + Bφ(a)时，对于所有a,B∈Α，当AB + BA = 0时，我们说φ是在零点处的约当可导映射。本文证明了如果φ是在零点处的约当可导映射，则存在一个导数δ:algMβ→M和一个标量λ∈C，使得对于algMβ中的所有a， φ(a)=δ(a) +λ a。

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Jordan Derivable Mappings at Zero Point

Let β be an arbitrary non-trivial nest in any factor von Neumann algebra M; and φ: algMβ→M be a weakly continuous linear mapping. We say that φ is a Jordan derivable mapping at zero point if φ(AB + BA) = φ(A)B + Aφ(B) +φ(B)A + Bφ(A) for all A,B∈Α with AB + BA = 0. In this paper, we prove that if φ is a Jordan derivable mapping at zero point, then there exist a derivation δ:algMβ→M and a scalar λ∈C such that φ(A)=δ(A) +λA for all A in algMβ.

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2010 International Conference on Computational Intelligence and Software Engineering

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