因子von Neumann代数上Jordan正交可导映射

设M是作用在维数大于2的复可分Hilbert空间H上的因子von Neumann代数。若φ:M→M上有界的Jordan正交可导线性映射,则存在数μ∈R,λ∈C和算子M∈M,且M+M*=μI,使得对所有的A∈M,有φ(A)=AM-MA+λA。若φ:M→M上有界的Jordan-*可导线性映射,则存在数μ∈R和算子T∈M,且T+T*=μI,使得对所有的A∈M,有φ(A)=AT-TA。

因子von Neumann代数上非线性~*-Jordan导子的刻画

在因子von Neumann代数Μ上给出了非线性~*-Jordan三重导子的定义,利用代数Pierce分解方法,证明了φ:Μ→Μ是非线性~*-Jordan导子当且仅当φ是非线性~*-Jordan三重导子.

Functional Inequalities in Non-Archimedean Normed Spaces

In this paper, we introduce an additive functional inequality and a quadratic functional inequality in normed spaces, and prove the Hyers-Ulam stability of the functional inequalities in Banach spaces. Furthermore, we introduce an additive functional inequality and a quadratic functional inequality in non-Archimedean normed spaces, and prove the Hyers-Ulam stability of the functional inequalities in non-Archimedean Banach spaces.

因子von Neumann代数上的κ-Jordan*映射

设A和B是两个因子von Neumann代数,k是n次单位根.证明了任意的A,B∈A,非线性双射Φ：A→B满足Φ（k（AB＋BA＊））=k（Φ（A）Φ（B）＋Φ（B）Φ（A）＊）当且仅当Φ是＊-环同构.