Representations of dynamical systems on Banach spaces not containing $l_1$
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- by E. Glasner and M. Megrelishvili PDF
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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.References
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Additional Information
- E. Glasner
- Affiliation: Department of Mathematics, Tel-Aviv University, Tel Aviv, Israel
- MR Author ID: 271825
- Email: glasner@math.tau.ac.il
- M. Megrelishvili
- Affiliation: Department of Mathematics, Bar-Ilan University, 52900 Ramat-Gan, Israel
- Email: megereli@math.biu.ac.il
- Received by editor(s): April 16, 2008
- Received by editor(s) in revised form: November 9, 2009, and January 21, 2011
- Published electronically: July 11, 2012
- Additional Notes: The first author’s research was partially supported by BSF (Binational USA-Israel) grant no. 2006119.
- © Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 364 (2012), 6395-6424
- MSC (2010): Primary 37Bxx, 54H20, 54H15, 46-xx
- DOI: https://doi.org/10.1090/S0002-9947-2012-05549-8
- MathSciNet review: 2958941