Lipschitz Spear Operators

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

Abstract

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

References

  1. 9.
    A. Avilés, V. Kadets, M. Martín, J. Merí, V. Shepelska, Slicely countably determined Banach spaces. Trans. Am. Math. Soc. 362, 4871–4900 (2010)MathSciNetCrossRefGoogle Scholar
  2. 10.
    J. Becerra, G. López, A. Rueda, Lipschitz slices versus linear slices in Banach spaces. Proc. Am. Math. Soc. 145, 1699–1708 (2017)MathSciNetMATHGoogle Scholar
  3. 17.
    T. Bosenko, Strong Daugavet operators and narrow operators with respect to Daugavet centers. Visn. Khark. Univ. Ser. Mat. Prykl. Mat. Mekh. 931(62), 5–19 (2010)MATHGoogle Scholar
  4. 18.
    T. Bosenko, V. Kadets, Daugavet centers. Zh. Mat. Fiz. Anal. Geom. 6, 3–20 (2010)MathSciNetMATHGoogle Scholar
  5. 46.
    G. Godefroy, A survey on Lipschitz-free Banach spaces. Comment. Math. 55, 89–118 (2015)MathSciNetMATHGoogle Scholar
  6. 48.
    G. Godefroy, N. Kalton, Lipschitz-free Banach spaces. Stud. Math. 159, 121–141 (2003)MathSciNetCrossRefGoogle Scholar
  7. 56.
    T. Ivashyna, Daugavet centers are separably determined. Mat. Stud. 40, 66–70 (2013)MathSciNetMATHGoogle Scholar
  8. 57.
    A. Jiménez-Vargas, J. Sepulcre, M. Villegas-Vallecillos, Lipschitz compact operators. J. Math. Anal. Appl. 415, 889–901 (2014)MathSciNetCrossRefGoogle Scholar
  9. 69.
    V. Kadets, M. Martín, J. Merí, D. Werner, Lipschitz slices and the Daugavet equation for Lipschitz operators. Proc. Am. Math. Soc. 143, 5281–5292 (2015)MathSciNetCrossRefGoogle Scholar
  10. 70.
    V. Kadets, A. Pérez, D. Werner, Operations with slicely countably determined sets. Funct. Approx. (to appear). arXiv:1708.05218
  11. 119.
    R. Wang, X. Huang, D. Tan, On the numerical radius of Lipschitz operators in Banach spaces. J. Math. Anal. Appl. 411, 1–18 (2014)MathSciNetCrossRefGoogle Scholar
  12. 120.
    N. Weaver, Lipschitz Algebras (Singapore, World Scientific, 1999)CrossRefGoogle Scholar
  13. 121.
    N. Weaver, On the unique predual problem for Lipschitz spaces. Math. Proc. Camb. Philos. Soc. (to appear). https://doi.org/10.1017/S0305004117000597

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

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