Anders Karlsson (Université de Genève) : "A new type of metric fixed point theorem"Séminaire « Géométrie dynamique »
Université de Genève, Suisse
Lieu : Salle Visio
Résumé : A general fixed point theorem for isometries in terms of metric functionals is proved under the assumption of the existence of a conical bicombing. One special case provides a new mean ergodic theorem that in the Hilbert space case implies von Neumann’s theorem. For CAT(0)-spaces and injective spaces the fixed point theorem is new for non-locally compact spaces, and implies the usual result for proper CAT(0)-spaces. For Banach spaces the theorem accommodates classically fixed-point-free isometric maps such as those of Kakutani, Edelstein, Alspach and Prus. It also leads to a result in the direction of the invariant subspace problem.