Mean Ergodic Theorems in Hilbert-Kaplansky spaces

TL;DR

This paper extends the mean ergodic theorem of von Neumann to Hilbert-Kaplansky spaces and introduces several variants including multiparameter, modulated, subsequential, and weighted versions.

Contribution

It provides the first proofs of various mean ergodic theorems in the setting of Hilbert-Kaplansky spaces, broadening ergodic theory applications.

Findings

Proved the mean ergodic theorem of von Neumann in Hilbert-Kaplansky spaces

Established multiparameter and weighted mean ergodic theorems in this setting

Extended ergodic theorems to modulated and subsequential cases

Abstract

We prove the mean ergodic theorem of von Neumann in a Hilbert-Kaplansky space. We also prove a multiparameter, modulated, subsequential and a weighted mean ergodic theorems in a Hilbert-Kaplansky space