标题： 关于$L^1$-逼近的群 显示英文标题

标题： On $L^1$-approximation of groups

摘要： 一个在群论和算子代数交叉领域的长期未解问题是，所有群是否都是MF群，即相对于算子范数被表示所逼近。 更一般地，对于 $1 \leq p \leq \infty$，Thom曾询问是否存在不被Schatten $p$-范数逼近的群。 $1 < p < \infty$的情况已在之前的研究中得到处理。 我们解决了 $p=1$的情况，解决了Lubotzky和Oppenheim遗漏的一个案例。 显示英文摘要

摘要： A longstanding open problem in the intersection of group theory and operator algebras is whether all groups are MF, that is, approximated by representations with respect to the operator norm. More generally, for $1 \leq p \leq \infty$, it has been asked by Thom whether there exist groups which are not approximated with respect to the Schatten $p$-norm. The cases of $1 < p < \infty$ were addressed in previous works. We settle the case $p=1$, solving a case left out by Lubotzky and Oppenheim.