希尔伯特空间的粗嵌入、Haagerup性质和Poincare不等式
Coarse embeddings into a Hilbert space, Haagerup Property and Poincare inequalities
摘要：
证明了度量空间不粗嵌入希尔伯特空间当且仅当它满足一系列Poincaré不等式，这些不等式可以用（广义）展开式表示.我们还给出了相对于压缩的定量陈述。在等变的上下文中，我们的结果表明，一个群不具有Haagerup性质当且仅当它具有关于一族概率的相对性质T，该概率族的支持度为无穷大。我们给这个结果的版本都在酉表示，并在希尔伯特空间上的仿射等距行动。
英文摘要：
We prove that a metric space does not coarsely embed into a Hilbert space if and only if it satisfies a sequence of Poincaré inequalities, which can be formulated in terms of (generalized) expanders. We also give quantitative statements, relative to the compression. In the equivariant context, our result says that a group does not have the Haagerup property if and only if it has relative property T with respect to a family of probabilities whose supports go to infinity. We give versions of this result both in terms of unitary representations, and in terms of affine isometric actions on Hilbert spaces.
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