标题： 全移位的间隙标签和渐近间隙开启 显示英文标题

标题： Gap Labels and Asymptotic Gap Opening for Full Shifts

摘要： 我们讨论由实数线的紧子集上的全移位生成的算子的间隙标记。 Johnson--Schwartzman间隙标记的集合是由单点分布支撑集的闭开子集的权重生成的代数。 由于存在周期轨道的稠密集，无法找到一个采样函数，使得所有由间隙标记定理允许的间隙同时打开。 然而，对于单点分布的适当选择，我们证明对于一般的采样函数，在大耦合极限下每个谱间隙都会打开。 此外，我们证明对于其他权重的选择，存在某些间隙无法在纯对角算子中打开。 显示英文摘要

摘要： We discuss gap labelling for operators generated by the full shift over a compact subset of the real line. The set of Johnson--Schwartzman gap labels is the algebra generated by weights of clopen subsets of the support of the single-site distribution. Due to the presence of a dense set of periodic orbits, it is impossible to find a sampling function for which all gaps allowed by the gap labelling theorem open simultaneously. Nevertheless, for a suitable choice of the single-site distribution, we show that for generic sampling functions, every spectral gap opens in the large-coupling limit. Furthermore, we show that for other choices of weights there are gaps that cannot open for purely diagonal operators.