arXiv subjects
Publications and source records attributed to Zhen Rong.
In this paper, we characterize mixing unilateral backward shifts on barrelled and ultrabarrelled topological sequence spaces respectively, which extend several well-known results in the existing literature. We present some nontrivial examples to show the validity of our results.
Extending previous results of Bourdon and Shapiro we characterize the hypercyclic and mixing composition operators $C_φ$ for the automorphisms of $\mathbb{D}$ on any of the spaces $H^{p}$ with $1\leqslant p<+\infty$.
Extending previous results of Godefroy and Shapiro we characterize the hypercyclic, mixing and chaotic conjugate multipliers on some reflexive spaces of analytic functions.
We study the independence density for finite families of finite tuples of sets for continuous actions of discrete groups on compact metrizable spaces. We use it to show that actions with positive naive entropy are Li-Yorke chaotic and untame. In particular, distal actions have zero naive entropy. This answers a question of Lewis Bowen.
Answering a question of Glasner, we show that any finitely generated nonabelian free group has a minimal null action which is a RIM non-open extension of an effective strongly proximal action.