A continuous operator acting on a topological vector space X is called hypercyclic provided there exists a vector x ∈ X such that its orbit {T nx; n ≥ 1} is dense in X. Such a vector is called a hypercyclic vector for T . The set of hypercyclic vectors will be denoted by HC(T ). The first example of hypercyclic operator was given by Birkhoff, 1929 [3], who shows that the operator of translation...

Chaotic linear dynamics deals primarily with various topological ergodic properties of semigroups of continuous linear operators acting on a topological vector space. We treat the questions of the following type. Characterize which of the spaces from a given class support a semigroup of prescribed shape satisfying a given topological ergodic property. In particular, we characterize LBS-spaces (...

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.