Eva Gallardo Gutiérrez (Université Complutense de Madrid) : The Cesàro operator: where are its invariant subspaces?

Lieu : salle Kampé de Fériet, 1er étage, Bâtiment M2

Date : vendredi 14 mars 2025

Heure : 14h

Oratrice : Eva Gallardo Gutiérrez

Affiliation : Université Complutense de Madrid

Titre : The Cesàro operator: where are its invariant subspaces?

--- Résumé ---

Despite the fact that one of the most classical transformations of sequences is the Cesàro operator C, there are still many questions about it unsettled. In the seventies, Kriete and Trutt proved the striking result that the Cesàro operator is subnormal, namely, C has a normal extension. Nonetheless, it remains unknown the description of the closed invariant subspaces of C.

In this talk, we will discuss the invariant subspaces of C in the Hardy spaces. Moreover, in the Hilbert space setting, by linking the invariant subspaces of C to the lattice of the closed invariant subspaces of the standard right-shift semigroup acting on a particular weighted L²-space on the line, we will exhibit a large class of non-trivial closed invariant subspaces of C and provide a complete characterization of the finite codimensional ones. In particular, we will establish the limits of such approach in order to provide a complete description of the lattice of the invariant subspaces of C.

Based on joint works with J. R. Partington and W. T. Ross.