广州数学大讲坛第十二期

第一百一十一讲——武汉大学王茂发教授学术报告

题目：HILBERT-SCHMIDTNESS OF DIFFERENCES OF COMPOSITION OPERATORS

时间：2022年11月2日（周三）下午16:40-17:40

地点：腾讯会议 （会议ID：590 194 848 密码：221104 ）

报告人：王茂发 教授

摘要：In the setting of the standard weighted Bergman spaces over the unit disk, compactness characterizations for linear combinations of composition operators have been known. One of those characterizations asserts that degenerate double differences, compared with each single difference, do not improve the compactness at all in the sense that a degenerate double difference is compact only when each difference is individually compact. Such a rigid phenomenon is actually known to hold for a certain broader class of linear combinations. In this talk we investigate into similar properties for Hilbert-Schmidtness with main focus on double differences.

We first obtain a complete characterization for Hilbert-Schmidt double differences of composition operators.

We then observe that double differences, compared with each single difference, can improve the Hilbert-Schmidtness even in the degenerate case, by constructing concrete examples of Hilbert-Schmidt double differences with each difference not being Hilbert-Schmidt. We also include some remarks concerning connections between Hilbert-Schmidtness on the standard weighted Bergman spaces and weak-to-strong boundedness on certain vector-valued weighted Bergman spaces.

报告人简介：

王茂发，武汉大学数学与统计杏吧传媒 教授，博士生导师。主要研究方向是泛函分析及其应用。先后承担国家自然科学基金重点项目、面上项目等多项，已在Sci. China Math.、 J. Funct. Anal.、Math. Z.、Indiana Univ. Math. J.、J Operator Theory等期刊上发表学术论文数十篇。