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math.FA2026
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…
math.FA2025
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…
math.FA2024
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…
math.FA2024
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…