报告人简介：

何莉，广州大学教授，博士生导师。主要从事函数空间上的算子与算子代数研究，近年来围绕解析 Sobolev 型空间及其上的算子与算子代数重要公开问题做了一系列重要工作，取得了突破性进展，在 J. Funct. Anal.、 Math. Z.、J. Operator Theory、 Proc. Amer. Math. Soc.、Bull. London. Math. Soc.、 Banach J. Math. Anal.等数学期刊上发表学术论文30余篇。主持国家自然科学基金青年项目1项、国家自然科学基金面上项目2项、广东省教育厅项目1项，广州市教育局项目1项。曾被评为“广州大学最受学生欢迎的老师”，获“第二届全国高校微课教学比赛广东省二等奖”。

报告简介：

This talk presents geometric characterizations of composition operators on holomorphic function spaces. Moving from reproducing kernel Hilbert spaces through Hardy–Sobolev spaces to general Banach spaces, we establish, under suitable structural hypotheses, that $C_\varphi$ is Fredholm if and only if $\varphi$ is an automorphism. The unified approach avoids explicit kernel estimates.

We then study closed range and essential norms on weighted Dirichlet spaces. For bounded operators with nonconstant symbols and $-1<\alpha<0$, reverse Carleson inequalities characterize closed range. Under the Compact-Hole Condition, this is equivalent to the image containing a complete outer annulus; under a Uniform Tail Condition, it is equivalent to uniform weighted area density. Finally, for $\alpha>-1$, we present essential norm estimates and an exact boundary-tail formula.