Noncommutative spherical maximal inequality associated with automorphisms

TL;DR

This paper extends classical spherical maximal inequalities to the noncommutative setting of von Neumann algebras, providing new bounds related to automorphisms.

Contribution

It introduces a noncommutative spherical maximal inequality associated with automorphisms, expanding the scope of previous discrete inequalities.

Findings

Established a noncommutative spherical maximal inequality.

Extended Magyar-Stein-Wainger's discrete inequality to noncommutative algebras.

Provides bounds for automorphisms on von Neumann algebras.

Abstract

In this paper, we establish a noncommutative spherical maximal inequality associated with automorphisms on von Neumann algebras, extending Magyar-Stein-Wainger's discrete spherical maximal inequality to the noncommutative setting.