Some Stability Results

  • Vladimir Kadets
  • Miguel Martín
  • Javier Merí
  • Antonio Pérez
Part of the Lecture Notes in Mathematics book series (LNM, volume 2205)


Let X, Y be Banach spaces. We denote by Lip0(X, Y ) the set of all Lipschitz mappings F : XY such that F(0) = 0. This is a Banach space when endowed with the norm


  1. 22.
    K. Boyko, V. Kadets, M. Martín, J. Merí, Properties of lush spaces and applications to Banach spaces with numerical index 1. Stud. Math. 190, 117–133 (2009)MathSciNetCrossRefGoogle Scholar
  2. 26.
    P. Cembranos, J. Mendoza, Banach Spaces of Vector-Valued Functions. Lecture Notes in Mathematics, vol. 1676 (Springer, Berlin, 1997)CrossRefGoogle Scholar
  3. 54.
    S. Heinrich, Ultraproducts in Banach space theory. J. Reine Angew. Math. 313, 72–104 (1980)MathSciNetMATHGoogle Scholar
  4. 67.
    V. Kadets, M. Martín, J. Merí, V. Shepelska, Lushness, numerical index one and duality. J. Math. Anal. Appl. 357, 15–24 (2009)MathSciNetCrossRefGoogle Scholar
  5. 94.
    M. Martín, T. Oikhberg, An alternative Daugavet property. J. Math. Anal. Appl. 294, 158–180 (2004)MathSciNetCrossRefGoogle Scholar
  6. 95.
    M. Martín, R. Payá, Numerical index of vector-valued function spaces. Stud. Math. 142, 269–280 (2000)MathSciNetCrossRefGoogle Scholar
  7. 96.
    M. Martín, R. Payá, On CL-spaces and almost-CL-spaces. Ark. Mat. 42, 107–118 (2004)MathSciNetCrossRefGoogle Scholar
  8. 97.
    M. Martín, A. Villena, Numerical index and Daugavet property for L (μ, X). Proc. Edinb. Math. Soc. 46, 415–420 (2003)Google Scholar
  9. 124.
    D. Werner, Recent progress on the Daugavet property. Irish. Math. Soc. Bull. 46, 77–97 (2001)MathSciNetMATHGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Vladimir Kadets
    • 1
  • Miguel Martín
    • 2
  • Javier Merí
    • 2
  • Antonio Pérez
    • 3
  1. 1.School of Mathematics and Computer ScienceV. N. Karazin Kharkiv National UniversityKharkivUkraine
  2. 2.Departamento de Análisis MatemáticoUniversidad de GranadaGranadaSpain
  3. 3.Departamento de MatemáticasUniversidad de MurciaMurciaSpain

Personalised recommendations