Seminario di Analisi Complessa
Dipartimento di Matematica
Università di Roma Tor Vergata
Prossimi seminari:
Anders Karlsson, Genéve. A fixed point theorem for isometries of metric spaces
Mercoledì 10 aprile ore 16 aula A0
Abstract:
Any isometry of a metric spaces must have a fixed point in a certain canonical compactification of the space. This result is more concrete if the space admits a convex bicombing, such as the lines in a Banach space or geodesics in a space of nonpositive curvature. It applies to invertible bounded operators on a Hilbert space H acting on Pos, the space of positive operator on H, giving a non-trivial invariant metric functional. Another application is to mean ergodic theorems when the usual formulation fails. There are also other examples of diffeomorphims acting by isometry on certain spaces of Riemannian or Kähler metrics. Biholomorphisms provide yet another source of isometries, but in that setting the conclusion is somewhat less clear in general. For proper metric spaces, the compactification in question is the horofunction compactification. All terms will be defined and explained.