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

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 all band projections in the tensor product of two Dedekind complete Riesz spaces with weak order units.