1,485 research outputs found
Metric spaces nonembeddable into Banach spaces with the Radon-Nikod\'ym property and thick families of geodesics
We show that a geodesic metric space which does not admit bilipschitz
embeddings into Banach spaces with the Radon-Nikod\'ym property does not
necessarily contain a bilipschitz image of a thick family of geodesics. This is
done by showing that any thick family of geodesics is not Markov convex, and
comparing this result with results of Cheeger-Kleiner, Lee-Naor, and Li. The
result contrasts with the earlier result of the author that any Banach space
without the Radon-Nikod\'ym property contains a bilipschitz image of a thick
family of geodesics
Metric characterizations of superreflexivity in terms of word hyperbolic groups and finite graphs
We show that superreflexivity can be characterized in terms of bilipschitz
embeddability of word hyperbolic groups. We compare characterizations of
superreflexivity in terms of diamond graphs and binary trees. We show that
there exist sequences of series-parallel graphs of increasing topological
complexity which admit uniformly bilipschitz embeddings into a Hilbert space,
and thus do not characterize superreflexivity
Total subspaces with long chains of nowhere norming weak sequential closures
If a separable Banach space is such that for some nonquasireflexive
Banach space there exists a surjective strictly singular operator then for every countable ordinal the dual of contains a
subspace whose weak sequential closures of orders less than are
not norming over any infinite-dimensional subspace of and whose weak
sequential closure of order coincides with $X^*
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