动力C*包含的唯一伪期望
Unique Pseudo-Expectations for Dynamical $C^*$-Inclusions
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中文总结 AI 辅助
本文针对三类动力C*包含研究唯一伪期望性质，旨在通过更多示例推动非周期性与唯一伪期望性质、忠实唯一伪期望性质与范数性关系等开放问题的解决。
中文摘要 AI 辅助
设(𝒜,G,α)为C*动力系统，C*包含𝒜⊆𝒜⋊_{α,r}G的唯一扩张性质已被广泛研究。本文研究其他自然的“动力”C*包含的唯一扩张性质，即：• C*_r(G)⊆𝒜⋊_{α,r}G；• 𝒜^G⊆𝒜，其中𝒜^G为不动点子代数；• Z(𝒜)^c⊆𝒜⋊_{α,r}G，其中Z(𝒜)^c=Z(𝒜)'∩(𝒜⋊_{α,r}G)是中心的相对交换子。本文希望更多样的示例能推动遗留开放问题的进展，特别是(1)非周期性与唯一伪期望性质的关系，(2)忠实唯一伪期望性质与范数性的关系。
英文摘要
Let $(\mathcal{A},G,α)$ be a $C^*$-dynamical system. Unique extension properties for the $C^*$-inclusion $\mathcal{A} \subseteq \mathcal{A} \rtimes_{α,r} G$ have been studied extensively. In this paper, we investigate unique extension properties for some other natural ``dynamical'' $C^*$-inclusions, namely: $\bullet$ $C_r^*(G) \subseteq \mathcal{A} \rtimes_{α,r} G$; $\bullet$ $\mathcal{A}^G \subseteq \mathcal{A}$, where $\mathcal{A}^G$ is the fixed-point subalgebra; $\bullet$ $Z(\mathcal{A})^c \subseteq \mathcal{A} \rtimes_{α,r} G$, where $Z(\mathcal{A})^c = Z(\mathcal{A})' \cap (\mathcal{A} \rtimes_{α,r} G)$ is the relative commutant of the center. Our hope is that a larger selection of examples will enable progress on some lingering open problems, in particular (1) the relationship between aperiodicity and the unique pseudo-expectation property and (2) the relationship between the faithful unique pseudo-expectation property and norming.
