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Embedding $\ell_1$ as Lipschitz functions


Author: M. Raja
Journal: Proc. Amer. Math. Soc. 133 (2005), 2395-2400
MSC (2000): Primary 46B20, 46B22, 54E99
DOI: https://doi.org/10.1090/S0002-9939-05-07943-8
Published electronically: March 15, 2005
MathSciNet review: 2138882
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Abstract: Let $K$ be a compact Hausdorff space and let $d$ be a lower semicontinuous metric on it. We prove that $K$ is fragmented by $d$ if, and only if, $C(K)$ contains no copy of $\ell_1$ made up of Lipschitz functions with respect to $d$. As applications we obtain a characterization of Asplund Banach spaces and Radon-Nikodým compacta.


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Additional Information

M. Raja
Affiliation: Einstein Institute of Mathematics, The Hebrew University of Jerusalem, Givat Ram, 91904, Jerusalem, Israel
Address at time of publication: Departamento de Matemáticas, Universidad de Murcia, Campus de Espinardo, 30100 Espinardo, Murcia, Spain
Email: matias@um.es

DOI: https://doi.org/10.1090/S0002-9939-05-07943-8
Received by editor(s): March 23, 2004
Published electronically: March 15, 2005
Additional Notes: This research was supported by a grant of Professor J. Lindenstrauss from the Israel Science Foundation, and by research grant BFM2002-01719, MCyT (Spain).
Communicated by: N. Tomczak-Jaegermann
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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