Disjoint and simultaneous hypercyclic Rolewicz-type operators

Authors : Nurhan ÇOLAKOĞLU, Özgür MARTİN

Pages : 1609-1619

Doi:10.15672/hujms.791344

View : 13 | Download : 7

Publication Date : 2021-12-14

Article Type : Research Paper

Abstract :We characterize disjoint hypercyclic and supercyclic tuples of unilateral Rolewicz-type operators on $c_0insert ignore into journalissuearticles values(\N);$ and $\ell^pinsert ignore into journalissuearticles values(\N);$, $p \in [1, \infty);$, which are a generalization of the unilateral backward shift operator. We show that disjoint hypercyclicity and disjoint supercyclicity are equivalent among a subfamily of these operators and disjoint hypercyclic unilateral Rolewicz-type operators always satisfy the Disjoint Hypercyclicity Criterion. We also characterize simultaneous hypercyclic unilateral Rolewicz-type operators on $c_0insert ignore into journalissuearticles values(\N);$ and $\ell^pinsert ignore into journalissuearticles values(\N);$, $p \in [1, \infty);$.
Keywords : hypercyclic vectors, hypercyclic operators, disjoint hypercyclicity, simultaneous hypercyclicity