Noncommutative discrete spherical maximal inequalities over a lacunary sequence

Abstract This paper establishes the noncommutative maximal inequality for discrete spherical averages over a lacunary sequence. Our main result extends the work of Hughes [J. Anal. Math. 138 (2019), no. 1, 1‐21] to the noncommutative setting and, meanwhile, strengthens the recent study of Chen and Hong [arXiv: 2410.06035 (2024)] to the case of .