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A characterization of superreflexivity through embeddings of lamplighter groups. (arXiv:1807.06692v1 [math.FA])
来源于:arXiv
We prove that finite lamplighter groups
$\{\mathbb{Z}_2\wr\mathbb{Z}_n\}_{n\ge 2}$ with a standard set of generators
embed with uniformly bounded distortions into any non-superreflexive Banach
space, and therefore form a set of test-spaces for superreflexivity. Our proof
is inspired by the well known identification of Cayley graphs of infinite
lamplighter groups with the horocyclic product of trees. We cover
$\mathbb{Z}_2\wr\mathbb{Z}_n$ by three sets with a structure similar to a
horocyclic product of trees, which enables us to construct well-controlled
embeddings. 查看全文>>