352 research outputs found
A new metric invariant for Banach spaces
We show that if the Szlenk index of a Banach space is larger than the
first infinite ordinal or if the Szlenk index of its dual is larger
than , then the tree of all finite sequences of integers equipped with
the hyperbolic distance metrically embeds into . We show that the converse
is true when is assumed to be reflexive. As an application, we exhibit new
classes of Banach spaces that are stable under coarse-Lipschitz embeddings and
therefore under uniform homeomorphisms.Comment: 22 page
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