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Free Banach spaces and the approximation properties


Authors: Gilles Godefroy and Narutaka Ozawa
Journal: Proc. Amer. Math. Soc. 142 (2014), 1681-1687
MSC (2010): Primary 46B20; Secondary 46B28, 46B50
DOI: https://doi.org/10.1090/S0002-9939-2014-11933-2
Published electronically: February 18, 2014
MathSciNet review: 3168474
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Abstract: We characterize the metric spaces whose free spaces have the bounded approximation property through a Lipschitz analogue of the local reflexivity principle. We show that there exist compact metric spaces whose free spaces fail the approximation property.


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Additional Information

Gilles Godefroy
Affiliation: Institut de Mathématiques de Jussieu, 4 Place Jussieu, 75005 Paris, France
Email: godefroy@math.jussieu.fr

Narutaka Ozawa
Affiliation: RIMS, Kyoto University, 606-8502 Kyoto, Japan
Email: narutaka@kurims.kyoto-u.ac.jp

DOI: https://doi.org/10.1090/S0002-9939-2014-11933-2
Keywords: Lipschitz free space, approximation property
Received by editor(s): January 4, 2012
Received by editor(s) in revised form: June 18, 2012
Published electronically: February 18, 2014
Communicated by: Thomas Schlumprecht
Article copyright: © Copyright 2014 American Mathematical Society

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