# Skew-product dynamical systems for crossed product C⁎-algebras and their ergodic properties

@article{Vecchio2021SkewproductDS, title={Skew-product dynamical systems for crossed product C⁎-algebras and their ergodic properties}, author={Simone Del Vecchio and Francesco Fidaleo and Stefano De Rossi}, journal={Journal of Mathematical Analysis and Applications}, year={2021}, volume={503}, pages={125302} }

Abstract Starting from a discrete C ⁎ -dynamical system ( A , θ , ω o ) , we define and study most of the main ergodic properties of the crossed product C ⁎ -dynamical system ( A ⋊ α Z , Φ θ , u , ω o ∘ E ) , E : A ⋊ α Z → A being the canonical conditional expectation of A ⋊ α Z onto A , provided α ∈ Aut ( A ) commute with the ⁎-automorphism θ up to a unitary u ∈ A . Here, Φ θ , u ∈ Aut ( A ⋊ α Z ) can be considered as the fully noncommutative generalisation of the celebrated skew-product…

## 3 Citations

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## References

SHOWING 1-10 OF 39 REFERENCES

Ergodic properties of the Anzai skew-product for the noncommutative torus, Ergod

- Theory Dyn. Syst
- 2021

Strict ergodicity and transformation on the torus, Amer

- J. math
- 1961

A Fejér theorem for boundary quotients arising from algebraic dynamical systems, Ann

- Sc. Norm. Super. Pisa Cl. Sci
- 2021

Ergodic properties of the Anzai skew-product for the non-commutative torus

- MathematicsErgodic Theory and Dynamical Systems
- 2021

We provide a systematic study of a non-commutative extension of the classical Anzai skew-product for the cartesian product of two copies of the unit circle to the non-commutative 2-tori. In…

On the Uniform Convergence of Ergodic Averages for $$C^*$$-Dynamical Systems

- Mathematics
- 2020

We investigate some ergodic and spectral properties of general (discrete) $C^*$-dynamical systems $({\mathfrak A},\Phi)$ made of a unital $C^*$-algebra and a multiplicative, identity-preserving…

Uniform convergence of Cesàro averages for uniquely ergodic Cdynamical systems, Mediterr

- J. Math.,
- 2020

A Fejér theorem for boundary quotients arising from algebraic dynamical systems

- Mathematics
- 2019

A Fejer-type theorem is proved within the framework of $C^*$-algebras associated with certain irreversible algebraic dynamical systems. This makes it possible to strengthen a result on the structure…

Uniform Convergence of Cesaro Averages for Uniquely Ergodic C*-Dynamical Systems

- Medicine, Computer ScienceEntropy
- 2018

It is proved that the uniform convergence of Cesaro averages 1n∑k=0n−1λ−nΦ(a) for all values λ in the unit circle, which are not eigenvalues corresponding to “measurable non-continuous” eigenfunctions.

Infinite index extensions of local nets and defects

- Mathematics, Physics
- 2017

The subfactor theory provides a tool to analyze and construct extensions of Quantum Field Theories, once the latter are formulated as local nets of von Neumann algebras. We generalize some of the…