论文标题
关于$ C^*$ - 动力学系统的ergodic平均值的均匀收敛
On the uniform convergence of ergodic averages for $C^*$-dynamical systems
论文作者
论文摘要
我们研究了一般（离散）$ c^*$ - 动力系统$（{\ Mathfrak a}，φ）$的一些急性和光谱属性$（{\ mathfrak a}，φ）$相对于定点子代理，享有独特的eRgodicity属性。对于$ c^*$ - 动态系统享受上面提到的强大的千古属性，我们提供$λ$的条件。单位圆圈$ \ {z \ in {\ Mathbb c} \ mid | z | z | = 1 \} $以及相应的eigenspace $ {\ mathfrak a}_λ\ suere seque平均值$ \ left（\ frac1 {n} \ sum_ {k = 0}^{n-1}λ^{ - k}φ^k \ right）_ {n> 0} $，在norm中收敛点。我们还描述了一些来自量子概率的关键示例，可以将获得的结果应用到其中。
We investigate some ergodic and spectral properties of general (discrete) $C^*$-dynamical systems $({\mathfrak A},Φ)$ made of a unital $C^*$-algebra and a multiplicative, identity-preserving $*$-map $Φ:{\mathfrak A}\to{\mathfrak A}$, particularising the situation when $({\mathfrak A},Φ)$ enjoys the property of unique ergodicity with respect to the fixed-point subalgebra. For $C^*$-dynamical systems enjoying or not the strong ergodic property mentioned above, we provide conditions on $λ$ in the unit circle $\{z\in{\mathbb C}\mid |z|=1\}$ and the corresponding eigenspace ${\mathfrak A}_λ\subset{\mathfrak A}$ for which the sequence of Cesaro averages $\left(\frac1{n}\sum_{k=0}^{n-1}λ^{-k}Φ^k\right)_{n>0}$, converges point-wise in norm. We also describe some pivotal examples coming from quantum probability, to which the obtained results can be applied.
