Further Results

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

Abstract

Our goal here is to complement the previous chapter with some interesting results. We characterize lush operators when the domain space has the Radon-Nikodým Property or the codomain space is Asplund, and we get better results when the domain or the codomain is finite-dimensional or when the operator has rank one. Further, we study the behaviour of lushness, spearness and the aDP with respect to the operation of taking adjoint operators.

References

  1. 20.
    R. Bourgin, Geometric Aspects of Convex Sets with the Radon-Nikodym Property. Lecture Notes in Mathematics, vol. 993 (Springer, Berlin, 1983)CrossRefGoogle Scholar
  2. 21.
    K. Boyko, V. Kadets, M. Martín, D. Werner, Numerical index of Banach spaces and duality. Math. Proc. Camb. 142, 93–102 (2007)MathSciNetCrossRefGoogle Scholar
  3. 53.
    P. Harmand, D. Werner, D. Werner, M-Ideals in Banach Spaces and Banach Algebras. Lecture Notes in Mathematics, vol. 1547 (Springer, Berlin, 1993)Google Scholar
  4. 61.
    V. Kadets, R. Shvidkoy, G. Sirotkin, D. Werner, Banach spaces with the Daugavet property. Trans. Am. Math. Soc. 352, 855–873 (2000)MathSciNetCrossRefGoogle Scholar
  5. 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
  6. 94.
    M. Martín, T. Oikhberg, An alternative Daugavet property. J. Math. Anal. Appl. 294, 158–180 (2004)MathSciNetCrossRefGoogle 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