Maximal inequalities in noncommutative analysis
主 题: Maximal inequalities in noncommutative analysis
报告人: Quanhua Xu (Harbin Institute of Technology and Université de Franche-Comté)
时 间: 2017-11-14 15:00 - 2017-11-14 16:00
地 点: Lecture Hall, Jiayibing Building, Jingchunyuan 82, BICMR
\n\tMaximal\ninequalities are of paramount importance in analysis. Here "analysis" is understood\nin a wide sense and includes harmonic analysis, probability theory and ergodic\ntheory.
\n\tWe will consider in this survey talk\nthe analogues of some classical inequalities in the noncommutative analysis.\nThen the usual Lp<\/sub>-spaces are replaced by noncommutative Lp<\/sub>-spaces\nassociated to von Neumann algebras. The theory of noncommutative\nmartingale\/ergodic inequalities was remarkable developed in the last 20 years.\nMany classical results were successfully transferred to the noncommutative\nsetting. This theory has fruitful interactions with operator spaces, quantum\nstochastic analysis and noncommutative harmonic analysis. We will discuss some\nof these noncommutative results and explain certain substantial difficulties in\nproving them.
\n\tAfter the talk, Prof. Xu will give\nan introduction to the recruitment of Institute for Advanced Study in\nMathematics of Harbin Institute of Technology.