报告题目：   Lattice homomorphisms in harmonic analysis

摘    要：If $G$ is a locally compact group, then natural spaces such as ${\mathrm L}^1(G)$ or ${\mathrm M}(G)$ carry more structure than just that of a Banach algebra. They are also vector lattices, so that they are, in fact, Banach lattice algebras. Therefore, if they act by convolution on, say, ${\mathrm L}^p(G)$, it is a meaningful question to ask if the corresponding map  into the Banach lattice algebra ${\mathrm L}_{\mathrm r}({\mathrm L}^p(G))$ of regular operators on ${\mathrm L}^p(G)$ is not only an algebra homomorphism, but also a lattice homomorphism. Analogous questions can be asked in similar situations, such as the left regular representation of ${\mathrm M}(G)$.

In this lecture, we shall give an overview of how these questions have been tackled, and how this finally resulted in the rule of thumb that the answer tends to be affirmative whenever the question is meaningful.

This is joint work with Garth Dales and David Kok.

报 告 人：Marcel de Jeu教授    Leiden University and University of Pretoria

报告时间： 2019年6月19日下午16:00-16:40

报告地点： 数学科学学院三楼报告厅（数学楼304房间）

欢迎广大老师和同学光临！