For any countable group, and also for any locally compact second countable, compactly generated topological group, G, we show the existence of a “universal” hypercyclic (i.e. topologically transitive) representation on a Hilbert space, in the sense that it simultaneously models every possible ergodic probability measure preserving free action of G.

In this short note, we answer a question of Martin and Sanders [Integr. Equ. Oper. Theory, 85 (2) (2016), 191-220] by showing the existence disjoint frequently hypercyclic operators which fail to be weakly mixing and, therefore, satisfy Disjoint Hypercyclicity Criterion. We also show that given an operator $T$ such $T \oplus T$ is hypercyclic, set $S$ $T, S$ are but Criterion SOT dense in algeb...

We provide with criteria for a family of sequences operators to share frequently universal vector. These are inspired by the classical Frequent Hypercyclicity Criterion and recent criterion due Grivaux, Matheron Menet where periodic points play central role. As an application, we obtain any operator T in specific class acting on separable Banach space, necessary sufficient condition subset ? co...

In this paper, we study the linear dynamical properties of shift operators on some classes Segal algebras. Moreover, characterize hypercyclic generalized bilateral standard Hilbert module.