标题： 离散量子群的Fejér表示及其应用 显示英文标题

标题： Fejér representations for discrete quantum groups and applications

摘要： 我们证明了一个离散量子群$\mathbb{G}$具有逼近性质当且仅当其$C^*$-代数或冯诺依曼代数的卷积乘积满足类似费耶尔的表示。 作为应用，我们将文献中的几个结果扩展到具有逼近性质的离散量子群的背景下。 此外，我们提供了$\mathcal{B}(\ell^2(\mathbb{G}))$的不变$L^\infty(\widehat{\mathbb{G}})$-双模和$\mathcal{K}(\ell^2(\mathbb{G}))$的不变$C(\widehat{\mathbb{G}})$-双模的新特征，其中一些在群设置中是新的。 最后，我们研究了离散量子群作用的富比尼卷积乘积。 显示英文摘要

摘要： We prove that a discrete quantum group $\mathbb{G}$ has the approximation property if and only if a Fej\'{e}r-type representation holds for its $C^*$-algebraic or von Neumann algebraic crossed products. As applications, we extend several results from the literature to the context of discrete quantum groups with the approximation property. Additionally, we provide new characterizations of invariant $L^\infty(\widehat{\mathbb{G}})$-bimodules of $\mathcal{B}(\ell^2(\mathbb{G}))$ and invariant $C(\widehat{\mathbb{G}})$-bimodules of $\mathcal{K}(\ell^2(\mathbb{G}))$, some of which are new in the group setting. Finally, we study Fubini crossed products of discrete quantum group actions.