Abstract
In this paper, 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 Calderón-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.
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