Opis

• Tytuł:
  A family of distal functions and multipliers for strict ergodicity
• Twórca:
  Glasner, Eli
• Opis:
  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 $|\mathcal{W}|$.
• Dostępność obiektu:
  Dostęp otwarty
• Prawa: https://creativecommons.org/licenses/by-nd/4.0 ;
  Prawa autorskie (c) 2023 Eli Glasner
• Data:
  2023.06.23
• Typ:
  info:eu-repo/semantics/article;
  info:eu-repo/semantics/publishedVersion;
  Recenzowany artykuł
• Język:
  angielski
• Źródło:
  Topological Methods in Nonlinear Analysis; Vol 61, No 2 (June 2023); 661 - 680;
  1230-3429
• Wydawca:
  Nicolaus Copernicus University in Toruń
• Relacja: https://apcz.umk.pl/TMNA/article/view/44691/35871 ;https://apcz.umk.pl/TMNA/article/view/44691/35872
• Temat i słowa kluczowe:
  Fistal functions;
  the Weyl algebra;
  strict ergodicity;
  37B05, 37A05
• Identyfikator: https://apcz.umk.pl/TMNA/article/view/44691
• Dostawca danych:
  Akademicka Platforma Czasopism
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