The study titled “Disjoint and simultaneously hypercyclic pseudo-shifts” was published in the Journal of Mathematical Analysis and Applications by ITU Mathematics Engineering faculty member Assist. Prof. Dr. Nurhan Çolakoğlu.
Weighted shift operators have always been a rich source of examples and counterexamples in operator theory and, in particular, in linear dynamics which is an area that study the dynamical properties of continuous linear operators on topological vector spaces. Unfortunately, when it comes to joint dynamical notions as disjointness and simultaneousness for finitely many hypercyclic operators, the dynamics of weighted shifts turns out to be very limited. For example, it was shown that tuples of weighted shifts can never be disjoint weakly mixing or disjoint mixing, nor satisfy the Disjoint Hypercyclicity Criterion. In this paper, they study the joint dynamics of pseudo-shifts which is a generalization of weighted shifts in order to provide a new source of examples, unify the known results related to the shift operators, and provide new results for simultaneous hypercyclicity.