Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
Mobile Device Pairing
Green Open Access
Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Representations of dynamical systems on Banach spaces not containing $ l_1$


Authors: E. Glasner and M. Megrelishvili
Journal: Trans. Amer. Math. Soc. 364 (2012), 6395-6424
MSC (2010): Primary 37Bxx, 54H20, 54H15, 46-xx
Published electronically: July 11, 2012
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC (2010): 37Bxx, 54H20, 54H15, 46-xx

Retrieve articles in all journals with MSC (2010): 37Bxx, 54H20, 54H15, 46-xx


Additional Information

E. Glasner
Affiliation: Department of Mathematics, Tel-Aviv University, Tel Aviv, Israel
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

DOI: http://dx.doi.org/10.1090/S0002-9947-2012-05549-8
PII: S 0002-9947(2012)05549-8
Keywords: Baire one function, Banach representation of dynamical systems, enveloping semigroup, fragmentability, Rosenthal’s dichotomy, Rosenthal’s compact, Tame system
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.
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.