论文标题
属性（t），用于统一限制的表示和弱* - 不变均值的连续性
Property (T) for uniformly bounded representations and weak*-continuity of invariant means
论文作者
论文摘要
对于每个$ c \ geq 1 $，我们通过考虑均匀边界的表示$π$具有固定绑定$ |π| \ leq c $来定义Kazhdan的财产（t）。我们对该特性进行了系统的研究，并表明它的特征是在适当的系数空间上唯一不变的平均值的弱续率。对于可数组，我们证明，因此获得的财产家族在von Neumann代数水平上产生了不变的。此外，通过关注等级1谎言组的某些表示形式，我们表明$ \ operatotorname {sp}（n，1）$和$ f_ {4，-20} $允许在希尔伯特空间上适当地统一地利用Lipschitz仿制动作。
For every $c\geq 1$, we define a strengthening of Kazhdan's Property (T) by considering uniformly bounded representations $π$ with fixed bound $|π|\leq c$. We carry out a systematic study of this property and show that it can be characterised by the weak*-continuity of the unique invariant mean on a suitable space of coefficients. For countable groups, we prove that the family of properties thus obtained yield an invariant at the von Neumann algebra level. Moreover, by focusing on certain representations of rank 1 Lie groups, we show that $\operatorname{Sp}(n,1)$ and $F_{4,-20}$ admit proper uniformly Lipschitz affine actions on Hilbert spaces.
