报告题目： On products of symmetries acting on Hilbert spaces

报 告 人：张远航 教授（吉林大学）

报告时间：2026年5月21日（星期四）10:15—11:15

报告地点：6776永利集团115（大报告厅）    

校内联系人：石瑞 教授         联系方式：84708351-8315

报告摘要：Let $\mathcal{H}$ be a complex, separable Hilbert space (of finite or infinite dimension), and let $\mathcal{U}(\mathcal{H})$ denote the group of unitary operators on $\mathcal{H}$. A symmetry is, by definition, a unitary operator $J$ with $J^2=I$. Denote by $\textup{Sym}_k(\mathcal{H})$ the subset of $\mathcal{U}(\mathcal{H}) consisting of those operators expressible as a product of $k$ symmetries. It is known that $\mathcal{U}(\mathcal{H}) = \textup{Sym}_4(\mathcal{H})$ if $\dim \mathcal{H}=\infty$, while the only additional condition in finite dimensions is that the determinant be $\pm 1$. Of all the sets $\textup{Sym}_k(\mathcal{H})$ with $k\in \{1,2,3,4\}$, the case $k=3$ has been the most stubborn to characterise. Among other things, we investigate which elements of $\textup{Sym}_3(\mathcal{H})$ possess exactly two eigenvalues in the setting where $\mathcal{H}$ is finite-dimensional.

This talk is based on a joint work with Laurent Marcoux and Heydar Radjavi.

报告人简介：张远航，吉林大学数学学院教授，博士生导师，研究方向为算子理论和算子代数，目前主要研究兴趣是线性算子的结构、单核C*-代数分类、套代数的可逆元群连通性问题。研究成果发表于Bull. Lond. Math. Soc.、Canad. J. Math.、Integral Equations Operator Theory、J. Funct. Anal.、J. Noncommut. Geom.、J. Operator Theory、Math. Z.、Proc. Amer. Math. Soc.、Sci. China Math.、Studia Math.等期刊。