A noncommutative maximal inequality for ergodic averages along arithmetic sets

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