Embeddings of Levy Families into Banach Spaces
نویسنده
چکیده
We prove that if a metric probability space with a usual concentration property embeds into a Banach space X, then X has a proportional Euclidean subspace. In particular, this yields a new characterization of weak cotype 2. We also find optimal lower estimates on embeddings spaces with concentration properties (i.e. uniformly convex spaces) into l ∞, thus providing an ”isomorphic” extension to results of Gromov-Milman and also generalizing estimates of Carl-Pajor and Gluskin.
منابع مشابه
Embedding Levy Families into Banach Spaces
We prove that if a metric probability space with a usual concentration property embeds into a finite dimensional Banach space X , then X has a Euclidean subspace of a proportional dimension. In particular this yields a new characterization of weak cotype 2. We also find optimal lower estimates on embeddings of metric spaces with concentration properties into l ∞, generalizing estimates of Bourg...
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