PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
2006 | 104 | 2 | 223-283
Tytuł artykułu

Hereditarily non-sensitive dynamical systems and linear representations

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
For an arbitrary topological group G any compact G-dynamical system (G,X) can be linearly G-represented as a weak*-compact subset of a dual Banach space V*. As was shown in [45] the Banach space V can be chosen to be reflexive iff the metric system (G,X) is weakly almost periodic (WAP). In the present paper we study the wider class of compact G-systems which can be linearly represented as a weak*-compact subset of a dual Banach space with the Radon-Nikodým property. We call such a system a Radon-Nikodým (RN) system. One of our main results is to show that for metrizable compact G-systems the three classes: RN, HNS (hereditarily non-sensitive) and HAE (hereditarily almost equicontinuous) coincide. We investigate these classes and their relation to previously studied classes of G-systems such as WAP and LE (locally equicontinuous). We show that the Glasner-Weiss examples of recurrent-transitive locally equicontinuous but not weakly almost periodic cascades are actually RN. Using fragmentability and Namioka's theorem we give an enveloping semigroup characterization of HNS systems and show that the enveloping semigroup E(X) of a compact metrizable HNS G-system is a separable Rosenthal compact, hence of cardinality $ ≤ 2^{ℵ₀}$. We investigate a dynamical version of the Bourgain-Fremlin-Talagrand dichotomy and a dynamical version of the Todorčević dichotomy concerning Rosenthal compacts.
Słowa kluczowe
Twórcy
autor
  • Department of Mathematics, Tel-Aviv University, Ramat Aviv, Israel
  • Department of Mathematics, Bar-Ilan University, 52900 Ramat-Gan, Israel
Bibliografia
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_4064-cm104-2-5
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.