Characterisation of conditional weak mixing via ergodicity of the tensor product in Riesz Spaces

TL;DR

This paper characterizes conditional weak mixing in systems preserving conditional expectations through the ergodicity of tensor products in Riesz spaces, advancing the understanding of their structural properties.

Contribution

It provides a novel characterization of conditional weak mixing via ergodicity of tensor products in Dedekind complete Riesz spaces, linking two key concepts.

Findings

Conditional weak mixing is characterized by ergodicity of tensor products.

Components of weak order units in tensor products are characterized.

The results apply to Dedekind complete Riesz spaces with weak order units.

Abstract

We link conditional weak mixing and ergodicity of the tensor product in Riesz spaces. In particular, we characterise conditional weak mixing of a conditional expectation preserving system by the ergodicity of its tensor product with itself or other ergodic systems. In order to achieve this we characterise the components of the weak order units in the tensor product of two Dedekind complete Riesz spaces with weak order units.