Fixed point theorem for reflexive Banach spaces and uniformly convex non positively curved metric spaces


This article generalizes the work of Ballmann and Światkowski to the case of Reflexive Banach spaces and uniformly convex Busemann spaces, thus giving a new fixed point criterion for groups acting on simplicial complexes.

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I would like to thank Uri Bader for many discussions about property (T) and fixed point properties and for communicating the work of Nowak which motivated this article.

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Correspondence to Izhar Oppenheim.

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Oppenheim, I. Fixed point theorem for reflexive Banach spaces and uniformly convex non positively curved metric spaces. Math. Z. 278, 649–661 (2014).

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  • Fixed point theorem
  • Busemann space
  • Reflexive Banach space
  • Property (T)

Mathematics Subject Classification (2010)

  • 20F65