Q-Math Seminar
An insight into commutants, idempotents and structure of operators
Speaker: Francisco Javier González Doña (UC3M)Date: Wednesday, 26 March 2025 - 13:00Place: Room 2.2.D08, Universidad Carlos III de Madrid
Online: https://eu.bbcollab.com/guest/22f7877a774148a3aee3e398a4a86380 (active on request)
Abstract:
The structure of normal operators has been well understood since the 1970s, thanks to the spectral theorem. As a consequence of this result, strong connections between the (bi)commutant, the structure of invariant subspaces and the Borelian functional calculus arise. However, for non-normal operators on Banach spaces, this connection remains unclear and far from fully understood.
In this talk, we will sketch the aforementioned notions for normal operators, and will introduce some recent ideas to study the structure of general operators from this point of view. If time permits, we will also present some results in this direction for composition operators acting on the Hardy space of the unit disc, where techniques from geometric function theory play a prominent role.
