论文标题
操作员代数的图形产品的CCAP
The CCAP for graph products of operator algebras
论文作者
论文摘要
对于简单的图$γ$，对于Unital $ c^*$ - 带有Gns-Faithful状态的代数$（\ Mathbf {a} _v，φ_v）$ forVγ$，我们考虑降低的图形产品 $(\mathcal{A},φ)=*_{v,Γ}(\mathbf{A}_{v},φ_v)$ , and show that if every $C^*$-algebra $\mathbf{A}_{v}$ has the completely contractive approximation property (CCAP) and satisfies some additional condition, then the graph product has the CCAP也是如此。在自然案例中，施加的额外条件是满足的，例如，对于拥有CCAP的离散组$ g $的减少组$ c^*$ - 代数。 我们的结果是[命题4.11，25]中Ricard和Xu的结果的扩展，在这些结果下，他们在自由产品的相同条件下证明了这一结果。此外，我们的结果还扩展了[定理5.5，24]中Reckwerdt的结果，在该群体下，他证明了在图形产品下保留了弱化的companity consance $ 1 $的小组。我们的结果进一步涵盖了许多来自Hecke-Elgebras和离散量子组的新案例。
For a simple graph $Γ$ and for unital $C^*$-algebras with GNS-faithful states $(\mathbf{A}_v,φ_v)$ for $v\in VΓ$, we consider the reduced graph product $(\mathcal{A},φ)=*_{v,Γ}(\mathbf{A}_{v},φ_v)$ , and show that if every $C^*$-algebra $\mathbf{A}_{v}$ has the completely contractive approximation property (CCAP) and satisfies some additional condition, then the graph product has the CCAP as well. The additional condition imposed is satisfied in natural cases, for example for the reduced group $C^*$-algebra of a discrete group $G$ that possesses the CCAP. Our result is an extension of the result of Ricard and Xu in [Proposition 4.11, 25] where they prove this result under the same conditions for free products. Moreover, our result also extends the result of Reckwerdt in [Theorem 5.5, 24], where he proved for groups that weak amenability with Cowling-Haagerup constant $1$ is preserved under graph products. Our result further covers many new cases coming from Hecke-algebras and discrete quantum groups.
