Noncommutative maximal ergodic theorems for positive contractions

作者：Bekjan Turdebek N^*

来源：Journal of Functional Analysis, 2008, 254(9): 2401-2418.

DOI：10.1016/j.jfa.2008.01.007

• noncommutative L-p-spaces
• noncommutative maximal ergodic theorems
• individual ergodic theorems

Let M be a von Neumann algebra equipped with a normal semifinite faithful trace tau. Let T be a positive linear contraction on M such that tau circle T <= tau and such that the numerical range of T as an operator on L-2(M) is contained in a Stoltz region with vertex 1. We show that Junge and Xu's noncommutative Stein maximal ergodic inequality holds for the powers of T on L-p(M), 1 < p <= infinity. We apply this result to obtain the noncommutative analogue of a recent result of Cohen concerning the iterates of the product of a finite number of conditional expectations.

• 出版日期2008-5-1
• 单位新疆大学