Inventiones mathematicae

, Volume 189, Issue 1, pp 143–148 | Cite as

A fixed point theorem for L 1 spaces

  • U. Bader
  • T. Gelander
  • N. MonodEmail author


We prove a fixed point theorem for a family of Banach spaces including notably L 1 and its non-commutative analogues. Several applications are given, e.g. the optimal solution to the “derivation problem” studied since the 1960s.


Banach Space Point Theorem Operator Algebra Point Property Isometric Action 
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  1. 1.
    Bader, U., Furman, A., Gelander, T., Monod, N.: Property (T) and rigidity for actions on Banach spaces. Acta Math. 198(1), 57–105 (2007) MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    Bekka, B., de la Harpe, P., Valette, A.: Kazhdan’s Property (T). New Mathematical Monographs, vol. 11. Cambridge University Press, Cambridge (2008) CrossRefGoogle Scholar
  3. 3.
    Cohen, P.J.: Factorization in group algebras. Duke Math. J. 26, 199–205 (1959) MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Connes, A., Weiss, B.: Property T and asymptotically invariant sequences. Israel J. Math. 37(3), 209–210 (1980) MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    Coronel, D., Navas, A., Ponce, M.: On bounded cocycles of isometries over a minimal dynamics. arXiv:1101.3523
  6. 6.
    Domínguez Benavides, T., Japón Pineda, M.A., Prus, S.: Weak compactness and fixed point property for affine mappings. J. Funct. Anal. 209(1), 1–15 (2004) MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    Haagerup, U.: All nuclear C -algebras are amenable. Invent. Math. 74(2), 305–319 (1983) MathSciNetzbMATHCrossRefGoogle Scholar
  8. 8.
    Kadison, R.V., Pedersen, G.K.: Means and convex combinations of unitary operators. Math. Scand. 57(2), 249–266 (1985) MathSciNetzbMATHGoogle Scholar
  9. 9.
    Kakutani, S.: Concrete representation of abstract (L)-spaces and the mean ergodic theorem. Ann. Math. (2) 42(2), 523–537 (1941) MathSciNetCrossRefGoogle Scholar
  10. 10.
    Konyagin, S.V.: A remark on renormings of nonreflexive spaces and the existence of a Chebyshev center. Vestn. Mosk. Univ., Ser. Filos. 2, 81–82 (1988) MathSciNetGoogle Scholar
  11. 11.
    Losert, V.: The derivation problem for group algebras. Ann. Math. (2) 168(1), 221–246 (2008) MathSciNetzbMATHCrossRefGoogle Scholar
  12. 12.
    Namioka, I., Asplund, E.: A geometric proof of Ryll-Nardzewski’s fixed point theorem. Bull. Am. Math. Soc. 73, 443–445 (1967) MathSciNetzbMATHCrossRefGoogle Scholar
  13. 13.
    Ringrose, J.R.: Automatic continuity of derivations of operator algebras. J. Lond. Math. Soc. 5, 432–438 (1972) MathSciNetzbMATHCrossRefGoogle Scholar
  14. 14.
    Runde, V.: Lectures on Amenability. Lectures Notes in Mathematics, vol. 1774. Springer, Berlin (2002) zbMATHCrossRefGoogle Scholar
  15. 15.
    Takesaki, M.: Theory of Operator Algebras. I. Encyclopaedia of Mathematical Sciences, vol. 124. Springer, Berlin (2002). Reprint of the first (1979) edition, Operator Algebras and Non-commutative Geometry 5 zbMATHGoogle Scholar
  16. 16.
    Veselý, L.: For a dense set of equivalent norms, a non-reflexive Banach space contains a triangle with no Chebyshev center. Comment. Math. Univ. Carol. 42(1), 153–158 (2001) zbMATHGoogle Scholar
  17. 17.
    Yosida, K., Hewitt, E.: Finitely additive measures. Trans. Am. Math. Soc. 72, 46–66 (1952) MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.TechnionHaifaIsrael
  2. 2.Hebrew UniversityJerusalemIsrael
  3. 3.EPFLLausanneSwitzerland

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