Amenable groups与可单位性的几何观
Amenable groups and a geometric view on unitarisability
摘要：
研究了群的酉性，通过考察希尔伯特空间的正可逆算子在锥上的作用。这样，我们就对Gilles Pisier关于酉群的某些普适常数的存在性的一个结果给出了一个几何证明。通过构造一类测地度量空间中有限集的重心，利用等距性证明了顺从群作用的一个不动点定理。特别是，我们证明了unitable群的扩展顺从群是unitable和虚拟unitable意味着unitable和估计相应的普适常数。
英文摘要：
We investigate unitarisability of groups by looking at actions on the cone of positive invertible operators of a Hilbert space. This way, we give a geometric prove to a result by Gilles Pisier on the existence of some universal constants for unitarisable groups. By constructing barycenters for finite sets in a some class of geodesic metric spaces, we prove a fixed point theorem for actions of amenable groups by isometries. In particular, we show that extensions of unitarisable groups by amenable groups are unitarisable and virtual unitarisability implies unitarisability and estimate the corresponding universal constants.
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