A noncommutative maximal inequality for ergodic averages along arithmetic sets

TL;DR

This paper proves a noncommutative maximal inequality for ergodic averages along specific arithmetic sets, expanding the understanding of ergodic theory in noncommutative $L_p$ spaces for certain values of p.

Contribution

It introduces a novel noncommutative maximal inequality for ergodic averages along power sets, applicable to noncommutative $L_p$ spaces for p greater than the golden ratio.

Findings

Established a noncommutative maximal inequality for specific arithmetic sets

Extended ergodic theory results to noncommutative $L_p$ spaces

Applicable for p > (√5 + 1)/2, the golden ratio

Abstract

In this paper, we establish a noncommutative maximal inequality for ergodic averages with respect to the set $\{k^t|k=1,2,3,...\}$ acting on noncommutative $L_p$ spaces for $p>\frac{\sqrt{5}+1}{2}$.