Commutator criteria for strong mixing II. More general and simpler
Commutator criteria for strong mixing II. More general and simpler
复制标题
强混合换向器准则II．
DOI：
10.4067/s0719-06462019000100037
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发表时间：
2015
期刊：
影响因子：
--
通讯作者：
R. T. Aldecoa
中科院分区：
文献类型：
--
作者：
S. Richard;R. T. Aldecoa
基于交换子方法，我们给出了一个新的判据，证明了具有适当长度函数的拓扑群的酉表示的强混合性。我们的结果推广和统一了最近关于Hilbert空间中由酉算子U$和自伴算子H$诱导的离散流U^N N和连续流T T N N作为应用，我们提出了一个简短的替代证明（不使用卷积）的强混合性质的左正规表示的$\sigma$-紧局部紧群。
We present a new criterion, based on commutator methods, for the strong mixing property of unitary representations of topological groups equipped with a proper length function. Our result generalises and unifies recent results on the strong mixing property of discrete flows $\{U^N\}_{N\in\mathbb Z}$ and continuous flows $\{{\rm e}^{-itH}\}_{t\in\mathbb R}$ induced by unitary operators $U$ and self-adjoint operators $H$ in a Hilbert space. As an application, we present a short alternative proof (not using convolutions) of the strong mixing property of the left regular representation of $\sigma$-compact locally compact groups.