报告题目：Maximal and square inequalities in noncommutative analysis

报告人：Quanhua Xu  Harbin Institute of Technology and Universit´ e de Franche-Comt´ e

报告时间：5月25日  16:00

报告地点： Zoom ID:93775719317, 密码：123456

摘要：

Inequalities are of paramount importance in analysis. Here“analysis” is understood in a wide sense and includes functional analysis, harmonic analysis, probability and ergodic theories.

We will consider in this survey talk the analogues of some classical inequalities in the noncom-mutative setting. The theory of noncommutative analysis has been remarkably developed since 15 or so years. It has interesting interactions with operator spaces, quantum stochastic analysis,noncommutative harmonic analysis and quantum information theory.

We will discuss some of these noncommutative results and explain certain substantial difficulties in proving them. As illustration, we will concentrate our attention to the noncommutative maxi-mal Dunford-Schwartz ergodic inequality and the noncommutative Burkholder-Gundy martingaleinequality.

The talk is kept as elementary as possible and should be accessible to anyone with basic back-ground in analysis.