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

^*Corresponding author for this work

School of Mathematical Sciences

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

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10.1090/S0002-9947-2012-05549-8

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Representations of dynamical systems on Banach spaces not containing L ₁

Abstract

Keywords

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