Individual ergodic theorems in noncommutative Orlicz spaces

TL;DR

This paper proves an individual ergodic theorem within noncommutative Orlicz spaces linked to semifinite von Neumann algebras, expanding ergodic theory into a noncommutative functional analysis setting.

Contribution

It establishes the first individual ergodic theorem for noncommutative Orlicz spaces under specific conditions, broadening the scope of ergodic theorems in operator algebras.

Findings

Proves individual ergodic theorem in noncommutative Orlicz spaces

Extends ergodic theory to noncommutative functional spaces

Applicable to spaces with $( ext{delta}_2, ext{Delta}_2)$-condition

Abstract

For a noncommutative Orlicz space associated with a semifnite von Neumann algebra, a faithful normal semifnite trace and an Orlicz function satisfying $(\delta_2,\Delta_2)-$condition, an individual ergodic theorem is proved.