6 papers
Stable invariant measures in linear dynamics
Valentin Gillet
We study the existence of stable invariant measures for operators and strongly continuous semigroups of operators on Banach spaces admitting either a dense bilateral backward orbit…
Weak limit semigroup in operator theory and ergodic theory
Tanja Eisner, Valentin Gillet
We study the weak limit semigroup of an operator , i.e., the set of all operators being weak limit points of the powers of , in three different but related contexts: Koopman…
Linear dynamics of random products of weighted shifts
Valentin Gillet
The aim of this article is to study the dynamics of random products of weighted shifts on a separable Fréchet sequence space. That is, given a measure-preserving dynamical system $…
Linear dynamics of random products of operators
Valentin Gillet
We study the linear dynamics of the random sequence of the operators . These products depend on an ergodic m…
Similar operator topologies on the space of positive contractions
Valentin Gillet
In this article, we study the similarity of the Polish operator topologies , , $\texttt{SOT}\mbox{$_{*}$}$ and $\texttt{SOT}\mbox{$^{*}$}$ on the set of…
Typical properties of positive contractions and the invariant subspace problem
Valentin Gillet
In this paper, we first study some elementary properties of a typical positive contraction on for the Strong Operator Topology and the Strong* Operator Topology. Using the…