Notes on ergodic theorems in non-commutative symmetric spaces

TL;DR

This paper proves an individual ergodic theorem for positive kernels on non-commutative symmetric spaces, extending ergodic theory to a broader non-commutative setting.

Contribution

It introduces ergodic theorems for positive kernels in non-commutative symmetric spaces, a novel extension of classical ergodic results.

Findings

Established ergodic theorem for DS+ operators on non-commutative spaces

Extended ergodic theory to non-commutative symmetric spaces

Provided new tools for analysis in non-commutative functional analysis

Abstract

In this paper we establish individual ergodic theorem for positive kernels (or so called Danford Shwartz (DS+) operators acting on non commutative symmetric spaces.