• Medientyp: E-Artikel
  • Titel: A spectral strong approximation theorem for measure-preserving actions
  • Beteiligte: ABÉRT, MIKLÓS
  • Erschienen: Cambridge University Press (CUP), 2020
  • Erschienen in: Ergodic Theory and Dynamical Systems, 40 (2020) 4, Seite 865-880
  • Sprache: Englisch
  • DOI: 10.1017/etds.2018.63
  • ISSN: 0143-3857; 1469-4417
  • Entstehung:
  • Anmerkungen:
  • Beschreibung: Let$\unicode[STIX]{x1D6E4}$be a finitely generated group acting by probability measure-preserving maps on the standard Borel space$(X,\unicode[STIX]{x1D707})$. We show that if$H\leq \unicode[STIX]{x1D6E4}$is a subgroup with relative spectral radius greater than the global spectral radius of the action, then$H$acts with finitely many ergodic components and spectral gap on$(X,\unicode[STIX]{x1D707})$. This answers a question of Shalom who proved this for normal subgroups.