We establish the quantitative mean ergodic theorems for two subclasses of power bounded operators on a fixed noncommutative Lp-space with 1<p<∞, which mainly concerns power bounded invertible operators and Lamperti contractions. Our approach to the quantitative ergodic theorems relies on noncommutative square function inequalities. The establishment of the latter involves several new ingredients such as the almost orthogonality and Calder\'on-Zygmund arguments for non-smooth kernels from semi-commutative harmonic analysis, the extension properties of the operators under consideration from operator theory, and a noncommutative version of the classical transference method due to Coifman and Weiss.

报告人简介：Bang Xu is a postdoctoral fellow at the University of Houston. He received his doctorate from Wuhan University in 2021. His main research interests are harmonic analysis and functional analysis.