Disjoint frequently hypercyclic pseudo-shifts

Difference sets and frequently hypercyclic weighted shifts

We solve several problems on frequently hypercyclic operators. Firstly, we characterize frequently hypercyclic weighted shifts on l(Z), p ≥ 1. Our method uses properties of the difference set of a set with positive upper density. Secondly, we show that there exists an operator which is U-frequently hypercyclic, yet not frequently hypercyclic and that there exists an operator which is frequently...

About Subspace-Frequently Hypercyclic Operators

In this paper, we introduce subspace-frequently hypercyclic operators. We show that these operators are subspace-hypercyclic and there are subspace-hypercyclic  operators that are not subspace-frequently hypercyclic. There is a criterion like to subspace-hypercyclicity criterion that implies subspace-frequent hypercyclicity and if an operator $T$ satisfies this criterion, then $Toplus T$ is sub...

Hypercyclic Behaviour of Operators in a Hypercyclic C0-Semigroup

Let {Tt}t≥0 be a hypercyclic strongly continuous semigroup of operators. Then each Tt (t > 0) is hypercyclic as a single operator, and it shares the set of hypercyclic vectors with the semigroup. This answers in the affirmative a natural question concerning hypercyclic C0-semigroups. The analogous result for frequent hypercyclicity is also obtained.

Generating Phase Shifts from Pseudo State Energy Shifts

A Universal Hypercyclic Representation

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.