Corpus ID: 207852694

Ergodic theory of affine isometric actions on Hilbert spaces

@article{Arano2019ErgodicTO,
  title={Ergodic theory of affine isometric actions on Hilbert spaces},
  author={Yuki Arano and Yusuke Isono and A. Marrakchi},
  journal={arXiv: Dynamical Systems},
  year={2019}
}
The classical Gaussian functor associates to every orthogonal representation of a locally compact group $G$ a probability measure preserving action of $G$ called a Gaussian action. In this paper, we generalize this construction by associating to every affine isometric action of $G$ on a Hilbert space, a one-parameter family of nonsingular Gaussian actions whose ergodic properties are related in a very subtle way to the geometry of the original action. We show that these nonsingular Gaussian… Expand