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
Galois Correspondence and Fourier Analysis on Local Discrete Subfactors
Discrete subfactors include a particular class of infinite index subfactors and all finite index ones. A discrete subfactor is called local when it is braided and it fulfills a commutativity
Invariant Conditional Expectations and Unique Ergodicity for Anzai Skew-Products
Anzai skew-products are shown to be uniquely ergodic with respect to the fixed-point subalgebra if and only if there is a unique conditional expectation onto such a subalgebra which is invariant
Spectral and ergodic properties of completely positive maps and decoherence
In an attempt to propose more general conditions for decoherence to occur, we study spectral and ergodic properties of unital, completely positive maps on not necessarily unital C∗algebras, with a

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
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
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
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
TLDR
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
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
...
1
2
3
4
...