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

@inproceedings{Homann2021CharacterisationOC, title={Characterisation of conditional weak mixing via ergodicity of the tensor product in Riesz Spaces}, author={Jonathan Homann and Wen-Chi Kuo and B. A. Watson}, year={2021} }

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.

## References

SHOWING 1-10 OF 25 REFERENCES

AN f-ALGEBRA APPROACH TO THE RIESZ TENSOR PRODUCT OF ARCHIMEDEAN RIESZ SPACES

- Mathematics
- 1989

Abstract We construct the Riesz tensor product of Archimedean Riesz spaces and derive its properties using functional calculus and f-algebras. We improve results on the approximation of elements in…

Conditional expectations on Riesz spaces

- Mathematics
- 2005

Abstract Conditional expectations operators acting on Riesz spaces are shown to commute with a class of principal band projections. Using the above commutation property, conditional expectation…

Tensor products of Archimedean partially ordered vector spaces

- Mathematics
- 2010

We study the tensor product of two directed Archimedean partially ordered vector spaces X and Y by means of Riesz completions. With the aid of the Fremlin tensor product of the Riesz completions of X…

The tensor product of f-algebras

- Mathematics
- 2017

Abstract In this paper we prove that the Fremlin tensor product of two f-algebras can be endowed with an f-algebra structure and satisfies an appropriate universal property. In particular, the Riesz…

Ergodic theory and the Strong Law of Large Numbers on Riesz spaces

- Mathematics
- 2007

Abstract In [W.-C. Kuo, C.C.A. Labuschagne, B.A. Watson, Discrete-time stochastic processes on Riesz spaces, Indag. Math. (N.S.) 15 (3) (2004) 435–451], we introduced the concepts of conditional…

Mixingales on Riesz spaces

- Mathematics
- 2013

Abstract A mixingale is a stochastic process which combines properties of martingales and mixing sequences. McLeish introduced the term mixingale at the 4th Conference on Stochastic Processes and…

Mixing inequalities in Riesz spaces

- Mathematics
- 2017

Various topics in stochastic processes have been considered in the abstract setting of Riesz spaces, for example martingales, martingale convergence, ergodic theory, AMARTS, Markov processes and…

Lp-spaces with respect to conditional expectation on Riesz spaces

- Mathematics
- 2017

Recently, Labuschagne and Watson introduced the space L2(T) for a conditional expectation T with natural domain a Riesz space L1(T). The main purpose of this paper is to carry on with this process by…

Tensor Products of f-algebras

- Mathematics
- 2016

We construct the tensor product for f-algebras, including proving a universal property for it, and investigate how it preserves algebraic properties of the factors.

Riesz Spaces, II

- Mathematics
- 1983

11. Prime Ideal Extension. 12. Order Bounded Operators. 13. Kernel Operators. 14. Normed Riesz Spaces. 15. Order Continuous Norms. 16. Embedding in Biduals. 17. Abstract L p Spaces. 18. Compact…