Operational 2-local automorphisms/derivations
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:王利广(曲阜师范大学)
:2024-07-30 15:15
:海韵园数理大楼686会议室
报告人:王利广(曲阜师范大学)
时 间:2024年7月30日15:15
地 点:海韵园数理大楼686会议室
内容摘要:
Let $\phi: \mathcal{A}\to \mathcal{A}$ be a (not necessarily linear, additive or continuous) map of a standard operator algebra. Suppose for any $a,b\in \mathcal{A}$ there is an algebra automorphism $\theta_{a,b}$ of $\mathcal{A}$ such that \begin{align*} \phi(a)\phi(b) = \theta_{a,b}(ab). \end{align*} We show that either $\phi$ or $-\phi$ is a linear Jordan homomorphism. Similar results are obtained when any of the following conditions is satisfied: \begin{align*} \phi(a) + \phi(b) &= \theta_{a,b}(a+b), \\ \phi(a)\phi(b)+\phi(b)\phi(a) &= \theta_{a,b}(ab+ba), \quad\text{or} \\ \phi(a)\phi(b)\phi(a) &= \theta_{a,b}(aba). \end{align*} We also show that a map $\phi: \mathcal{M}\rightarrow\mathcal{M}$ of a semi-finite von Neumann algebra $\mathcal{M}$ is a linear derivation if for every $a,b\in \mathcal{M}$ there is a linear derivation $D_{a,b}$ of $\mathcal{M}$ such that $$ \phi(a)b + a\phi(b) = D_{a,b}(ab).$$
个人简介:
王利广,曲阜师范大学教授。2005年7月于中国科学院获理学博士学位。研究方向为泛函分析和算子代数。主持完成国家自然科学基金面上项目两项,主持完成山东省自然科学基金面上项目两项。已在《J. Functional Analysis》、《J. Operator Theory》等期刊发表论文30余篇。
联系人:程庆进