A new type of fixed-point theorem in metric spaces (Anders Karlsson, UNIGE)

18.10.2022 10:30

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.

Lieu

Bâtiment: Conseil Général 7-9

Room 1-05, Tuesday 18.10.2022, Séminaire "Groupes et géométrie"

entrée libre