论文标题
不变的何时意味着Følner网的极限？
When is an invariant mean the limit of a Følner net?
论文作者
论文摘要
让$ g $为本地紧凑的木材群体，$ tlim（g）$ $ g $上的拓扑左右均值和$ tlim_0（g）$ folner-nets的限制点。我表明$ tlim_0（g）= tlim（g）$，除非$ g $是$σ$ -compact非偶像，在这种情况下，$ tlim_0（g）\ neq tlim（g）$。这改善了1970年的Chou和2009年Hindman和Strauss的结果。我考虑了非遗传左右流量的类似问题，并简化了净融合到不变性“微弱但不强烈”的简短结构，简化了罗森布拉特和威利斯2001年结果的证明。
Let $G$ be a locally compact amenable group, $TLIM(G)$ the topological left-invariant means on $G$, and $TLIM_0(G)$ the limit points of Folner-nets. I show that $TLIM_0(G) = TLIM(G)$ unless $G$ is $σ$-compact non-unimodular, in which case $TLIM_0(G) \neq TLIM(G)$. This improves a 1970 result of Chou and a 2009 result of Hindman and Strauss. I consider the analogous problem for the non-topological left-invariant means, and give a short construction of a net converging to invariance "weakly but not strongly," simplifying the proof of a 2001 result of Rosenblatt and Willis.
