Free Banach spaces and the approximation properties
By Gilles Godefroy, Nathanial P. Brown Narutaka Ozawa. 2012
59 citations recorded by the source corpus.
We characterize the metric spaces whose free space has 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.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/ba5f7f7dcfa484a35bb312d4fefb09d42d8e4c03
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In Geometry and Topology
In Mathematical Physics
Citations in the corpus
- Free Spaces Over Some Proper Metric Spaces (2014, background): “are not only positive results, Godefroy and Ozawa [7] constructed a compact metric space (K, d) such that F(K) fails the AP.”
- Lipschitz operator ideals and the approximation property (2016, background): “Although in recent years there is an increasing interest for finding results on approximation properties related to Lipschitz functions and the free spaces Æ(X) of metric spaces X (see [15, 16, 21, 22, 29]), there are no explicit definitions of approximation properties on metric spaces.”