论文标题
脱节性高度环境，sidon套装和弱混合操作员
Disjoint hypercyclicity, Sidon sets and weakly mixing operators
论文作者
论文摘要
我们证明，一组有限的自然数量$ j $满足$ j \ cup \ {0 \} $不是sidon，并且仅当任何操作员$ t $时，$ \ \ \ {t^j：j \} $ in J \} $ in J \ \} $的脱节超循环性意味着$ T $弱混合。作为一个应用程序，我们显示存在非弱混合操作员$ t $的存在，因此每个$ n $ $ t \ oplus t^2 \ ldots \ oplus t^n $都是超循环。
We prove that a finite set of natural numbers $J$ satisfies that $J\cup\{0\}$ is not Sidon if and only if for any operator $T$, the disjoint hypercyclicity of $\{T^j:j\in J\}$ implies that $T$ is weakly mixing. As an application we show the existence of a non weakly mixing operator $T$ such that $T\oplus T^2\ldots \oplus T^n$ is hypercyclic for every $n$.
