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

报 告 人：张远航（吉林大学）

报告时间：2025年4月19日上午9:00--10:00

报告地点：数学科学学院301室

报告摘要：Let $\hilb$ be a complex, separable Hilbert space (of finite or infinite dimension), and let $\cU(\hilb)$ denote the group of unitary operators on $\hilb$.   A symmetry is, by definition, a unitary operator $J$ with $J^2 =I$. Denote by $\symk(\hilb)$ the subset of $\cU(\hilb)$ consisting of those operators expressible as a product of $k$ symmetries. It is known that $\cU(\hilb) = \symfour(\hilb)$ if $\dim \, \hilb = \infty$, while the only additional condition in finite dimensions is that the determinant be $\pm 1$. Of all the sets $\symk(\hilb)$ 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 $\symthree(\hilb)$ possess exactly two eigenvalues in the setting where $\hilb$ 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，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J. Funct. Anal.、J. Noncommut. Geom.、J.Operator Theory、Math. Z.、Proc. Amer. Math. Soc.、Sci.China Math.、Studia Math及被Canad. J. Math.录用。