不相交超循环性、Sidon集与弱混合算子

Disjoint frequent hypercyclicity of composition operators

We give a sufficient condition for two operators to be disjointly frequently hypercyclic. We apply this criterion to composition operators acting on $H(\mathbb D)$ or on the Hardy space $H^2(\mathbb D)$. We simplify a result on disjoint frequent hypercyclicity of pseudo shifts of a recent paper of Martin et al. and we exhibit two disjointly frequently hypercyclic weighted shifts.

Disjoint hypercyclicity of weighted translations

Given a locally compact group $G$ and $1\leq p<\infty$, a sufficient condition ensuring the \emph{disjoint hypercyclicity} of finitely many weighted translations on $L^p(G)$ was investigated in this paper.

Disjoint and Simultaneously Hypercyclic Pseudo-Shifts

We characterize disjoint and simultaneously hypercyclic tuples of unilateral pseudo-shift operators on $\ell^p(\mathbb{N})$. As a consequence, complementing the results of Bernal and Jung, we give a characterization for simultaneously hypercyclic tuples of unilateral weighted shifts. We also give characterizations for unilateral pseudo-shifts that satisfy the Disjoint and Simultaneous Hypercyclicity Criterions. Contrary to the disjoint hypercyclicity case, tuples of weighted shifts turn out to be simultaneously hypercyclic if and only if they satisfy the Simultaneous Hypercyclicity Criterion.

Disjoint frequently hypercyclic pseudo-shifts

We obtain a Disjoint Frequent Hypercyclicity Criterion and show that it characterizes disjoint frequent hypercyclicity for a family of unilateral pseudo-shifts on $c_0(\mathbb{N})$ and $\ell^p(\mathbb{N})$, $1\le p <\infty$. As an application, we characterize disjoint frequently hypercyclic weighted shifts. We give analogous results for the weaker notions of disjoint upper frequent and reiterative hypercyclicity. Finally, we provide counterexamples showing that, although the frequent hypercyclicity, upper frequent hypercyclicity, and reiterative hypercyclicity coincide for weighted shifts on $…

Hilbert C-模上广义加权移位算子的频繁不相交超循环性与强拓扑传递性

Frequent, disjoint hypercyclicity and strong topological transitivity of generalized weighted shift operators on Hilbert C-modules

本文针对可分Hilbert空间上紧算子C-代数对应的标准Hilbert C-模，研究广义双边加权移位算子的频繁超循环准则、混沌、不相交超循环性及基于Furstenberg族的F-传递性等动力学性质。

沿滤子的不相交超循环性

Disjoint Hypercyclicity along filters

我们推广了Bès，Martin，Peris和Shkarin的一个结果：$B_w$是$\mathscr{F}$ -加权后移当且仅当对任何$r\in \mathbb{N}$，$(B_w,\dots, B_w^r)$是$d$ - $\mathscr{F}$，其中$\mathscr{F}$沿着严格包含上有限集族的滤子运行，这在拉姆齐理论中经常使用.另一方面，我们指出，这种现象不会发生超出加权移位框架，通过显示一个混合线性算子$T$的希尔伯特空间，使元组$(T, T^2)$是不是$d$ -syndetic。我们还研究了滤子$\mathscr{F}$包含在联集族中时，超循环算子与$d$ - $\mathscr{F}$元组之间的关系.最后，我们研究的条件，以获得迭代超循环从syndeticity加权移位框架。