Some noncommutative subsequential weighted individual ergodic theorems

TL;DR

This paper investigates convergence properties of subsequential weighted ergodic averages in noncommutative Lp-spaces, extending classical results to new types of sequences within the framework of von Neumann algebras.

Contribution

It establishes convergence of weighted ergodic averages along sequences with density one and block sequences with positive lower density in noncommutative Lp-spaces, extending prior uniform sequence results.

Findings

Convergence along sequences with density one.

Convergence along certain block sequences with positive lower density.

Extension of known results to noncommutative settings.

Abstract

This article is devoted to studying individual ergodic theorems for subsequential weighted ergodic averages on the noncommutative Lp-spaces associated to a semifinite von Neumann algebra M. In particular, we establish the convergence of these averages along sequences with density one and certain types of block sequences with positive lower density, and we extend known results along uniform sequences in the sense of Brunel and Keane.