Kazhdan投影的局部特征及其应用
A local characterization of Kazhdan projections and applications
摘要：
本文给出了紧生成局部紧群$G$的巴拿赫空间表示的任意族的Kazhdan投影存在性的局部刻划.我们还定义和研究自然推广的Fell拓扑任意巴拿赫空间表示的局部紧群。我们给出了几个应用方面的稳定性的刚性扰动。其中，我们给出了Delorme-Guichardet定理的一个Banach空间版本，证明了性质（T）和（FH）对于$σ$ -紧局部紧群是等价的.另一种应用是Banach强性质（T）的许多形式在标记群空间中是开的，更一般地说，每个具有这种性质的群都是具有相同性质的紧表现群的商。我们还研究了中心和非中心Kazhdan投影的概念，并给出了来自双曲群的非中心Kazhdan投影的例子。
英文摘要：
We give a local characterization of the existence of Kazhdan projections for arbitary families of Banach space representations of a compactly generated locally compact group $G$. We also define and study a natural generalization of the Fell topology to arbitrary Banach space representations of a locally compact group. We give several applications in terms of stability of rigidity under perturbations. Among them, we show a Banach-space version of the Delorme--Guichardet theorem stating that property (T) and (FH) are equivalent for $σ$-compact locally compact groups. Another kind of applications is that many forms of Banach strong property (T) are open in the space of marked groups, and more generally every group with such a property is a quotient of a compactly presented group with the same property. We also investigate the notions of central and non central Kazhdan projections, and present examples of non central Kazhdan projections coming from hyperbolic groups.
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