Representations of dynamical systems on Banach spaces not containing L 1

E. Glasner; M. Megrelishvili

doi:10.1090/S0002-9947-2012-05549-8

Representations of dynamical systems on Banach spaces not containing L ₁

E. Glasner, M. Megrelishvili

Tel Aviv University, Bar-Ilan University

Research output: Contribution to journal › Article › peer-review

Abstract

For a topological group G, we show that a compact metric G-space is tame if and only if it can be linearly represented on a separable Banach space which does not contain an isomorphic copy of l ₁ (we call such Banach spaces, Rosenthal spaces). With this goal in mind we study tame dynamical systems and their representations on Banach spaces.

Original language	English
Pages (from-to)	6395-6424
Number of pages	30
Journal	Transactions of the American Mathematical Society
Volume	364
Issue number	12
DOIs	https://doi.org/10.1090/S0002-9947-2012-05549-8
State	Published - 2012

Keywords

Baire one function
Banach representation of dynamical systems
Enveloping semigroup
Fragmentability
Rosenthal's compact
Rosenthal's dichotomy
Tame system

All Science Journal Classification (ASJC) codes

Applied Mathematics
General Mathematics

Access to Document

10.1090/S0002-9947-2012-05549-8

Cite this

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abstract = "For a topological group G, we show that a compact metric G-space is tame if and only if it can be linearly represented on a separable Banach space which does not contain an isomorphic copy of l 1 (we call such Banach spaces, Rosenthal spaces). With this goal in mind we study tame dynamical systems and their representations on Banach spaces.",

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