数学学科2019系列学术报告之五

报告人：Jani Virtanen
题目：Compact Hankel operators with bounded symbols
报告时间：4月25日15：00-16：00
地点：学科报告厅1-301

摘要：

        I discuss compactness of Hankel operators on Hardy, Bergman and Fock spaces with focus on the differences between the three cases. In particular, I present a new proof (based on limit operator techniques) of the result that the Hankel operator $H_f$ with a bounded symbol is compact on standard weighted Fock spaces if and only if $H_{/bar f}$ is compact. Our proof fully explains that this striking result is caused by the lack of bounded analytic functions in the complex plane (unlike in the other two spaces) and extends the result from the Fock-Hilbert space to all standard weighted Fock-Banach spaces. We also show that the compactness of Hankel operators is independent of the underlying space in all three cases. As an application, I discuss the role of compact Hankel operators in the study of the Fredholm properties of Toeplitz operators. This talk is based on joint work with Raffael Hagger.

        报告人简介：英国Reading大学教授、博士生导师，长期从事函数空间与算子理论的研究工作。