报告题目：Irreducible approximation of Toeplitz operators and matrices

　　报告人：朱森教授

　　报告时间：2023.12.7 14：30-15：30

　　报告地点：数学与统计学院 104报告厅

　　报告人简介：朱森，吉林大学数学学院教授，博士生导师. 主持国家自然科学基金青年、面上等项目. 近年来主要从事线性算子的复对称性、随机理论等方面的研究，在 J. Funct. Anal., J. London Math. Soc., Math. Ann., Math. Z, Sci. China Math., Trans. AMS等杂志发表系列论文.

　　报告内容简介：
　　The classification of the reducing subspaces of analytic Toeplitz operators on the classical Hardy space $H^2$ was completed in the 1970s due to work by Cowen and by Thomson. As for the reducing subspaces of non-analytic Toeplitz operators, to the best of our knowledge, there is no result in the literature so far.
　　We initiate to describe the reducing subspaces of Toeplitz operators via an approximation approach, showing that in the class of Toeplitz operators with continuous symbols those irreducible ones constitute a dense $G_\delta$. Our result depends on a finite-dimensional approximation result, which asserts that in the class of $n\times n$ Toeplitz matrices those irreducible ones constitute an open dense subset.