Free Banach spaces and the approximation properties
G Godefroy, N Ozawa - Proceedings of the American Mathematical Society, 2014 - ams.org
G Godefroy, N Ozawa
Proceedings of the American Mathematical Society, 2014•ams.org… 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. … We recall
that a Banach space X has the approximation property (AP) if the identity idX of X is in the
closure of the finite rank operators on X for the topology of uniform convergence on compact
sets. The λ-bounded …
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. … We recall
that a Banach space X has the approximation property (AP) if the identity idX of X is in the
closure of the finite rank operators on X for the topology of uniform convergence on compact
sets. The λ-bounded …
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. References
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