@article{Glasner_2023, title={A family of distal functions and multipliers for strict ergodicity}, volume={61}, url={https://apcz.umk.pl/TMNA/article/view/44691}, DOI={10.12775/TMNA.2022.030}, abstractNote={We give two proofs to an old result of E. Salehi, showing that the Weyl subalgebra $\mathcal{W}$ of $\ell^\infty(\Z)$ is a proper subalgebra of $\mathcal{D}$,
the algebra of distal functions. We also show that the family $\mathcal{S}^d$ of strictly ergodic functions in $\mathcal{D}$ does not form an algebra and hence in
particular does not coincide with $\mathcal{W}$.
We then use similar constructions to show that a function which is a multiplier for strict ergodicity,
either within $\mathcal{D}$ or in general, is necessarily a constant.
An example of a metric, strictly ergodic, distal flow is constructed which admits a non-strictly ergodic $2$-fold minimal self-joining.
It then follows that the enveloping group of this flow is not strictly ergodic (as a $T$-flow).
Finally we show that the distal, strictly ergodic Heisenberg nil-flow is relatively
disjoint over its largest equicontinuous factor from the universal Weyl flow $|\mathcal{W}|$.}, number={2}, journal={Topological Methods in Nonlinear Analysis}, author={Glasner, Eli}, year={2023}, month={Jun.}, pages={661–680} }