SEMINARIO DE ANÁLISIS COMPLEJO (COMPLEX ANALYSIS SEMINAR)

On commutants of composition operators embedded into C0−semigroups

Javier GONZÁLEZ DOÑA

Universidad Carlos III de Madrid

Wednesday, March 5, 2025 at 15:00
Room 520, Module 17, Department of Mathematics,
Universidad Autónoma de Madrid

Abstract:
Let Cϕ be a composition operator acting on the Hardy space of the unit disc Hp
(1 ≤ p < ∞), which is embedded in a C0-semigroup of composition operators T =
(Cϕ)t≥0. In this talk, we will study whether the commutant or the bicommutant of
Cϕ are isomorphic to subalgebras of continuous functions defined on a connected
set. In particular, it will allow us to derive results about the existence of non-trivial
idempotents (and non-trivial orthogonal projections if p = 2) lying in such sets. Our
methods, that depend heavily on the geometric properties of the associated Koenigs
domain Ω, also provide consequences regarding the extended eigenvalues of such
operators.