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SUMMARY:A fixed point theorem for isometries (Geometry Seminar)
DTSTART:20241218T111500
DTEND:20241218T121500
DTSTAMP:20260526T082808Z
UID:41785ea523394cdfc74cb6ebac1b3aa49d6a8b5487aad5289fe6034c
CATEGORIES:Conferences - Seminars
DESCRIPTION:Anders Karlsson\, UniGe\nA new fixed-point theorem will be exp
 lained asserting that every isometry of a metric space has a fixed-point i
 n the metric compactification of (the injective hull of) the space. In cas
 e the metric space admits a conical bicombing there is no need for passing
  to the injective hull\, examples of such spaces include all Banach spaces
 \, CAT(0)-spaces\, injective metric spaces\, spaces of positive operators\
 , as well as convex subsets and products thereof. The central notion is th
 at of a metric functional which is an extension of Busemann’s and Gromov
 ’s horofunctions. The result is in particular new for infinite-dimension
 al Banach spaces and non-proper CAT(0)-spaces. As a consequence\, well-kno
 wn fixed-point free examples get their fixed-point as it were. A new mean 
 ergodic theorem generalizing von Neumann’s is another direct consequence
 . A more elaborate corollary is that every invertible bounded linear opera
 tor of a Hilbert space admits a non-trivial invariant metric functional on
  the symmetric space of positive operators.
LOCATION:CH B3 31 https://plan.epfl.ch/?room==CH%20B3%2031
STATUS:CONFIRMED
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