Spear Vectors and Spear Sets

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

Abstract

The following definition will be crucial in our further discussion.

References

  1. 4.
    M. Acosta, J. Becerra, A. Rodriguez-Palacios, Weakly open sets in the unit ball of the projective tensor product of Banach spaces. J. Math. Anal. Appl. 383, 461–473 (2011)MathSciNetCrossRefGoogle Scholar
  2. 7.
    M. Ardalani, Numerical index with respect to an operator. Stud. Math. 224, 165–171 (2014)MathSciNetCrossRefGoogle Scholar
  3. 23.
    M. Cabrera, A. Rodríguez-Palacios, Non-associative normed algebras, Volume 1: The Vidav-Palmer and Gelfand-Naimark theorems, in Encyclopedia of Mathematics and Its Applications, vol. 154 (Cambridge University Press, Cambridge, 2014)Google Scholar
  4. 29.
    G. Choquet, Lectures on Analysis, Vol. 2: Representation Theory (W.A. Benjamin, New York, 1969)Google Scholar
  5. 35.
    J. Diestel, Sequences and Series in Banach Spaces. Graduate Texts in Mathematics, vol. 92 (Springer, New York/Heidelberg/Berlin, 1984), p. XIIICrossRefGoogle Scholar
  6. 38.
    M. Fabian, P. Habala, P. Hájek, V. Montesinos, V. Zizler, Banach Space Theory: The Basis for Linear and Nonlinear Analysis (Springer Science and Business Media, New York, 2011)CrossRefGoogle Scholar
  7. 40.
    V. Fonf, One property of Lindenstrauss-Phelps spaces. Funct. Anal. Appl. 13, 66–67 (1979)MathSciNetCrossRefGoogle Scholar
  8. 47.
    G. Godefroy, V. Indumathi, Norm-to-weak upper semicontinuity of the duality mapping and pre-duality mapping. Set-Valued Anal. 10, 317–330 (2002)MathSciNetCrossRefGoogle Scholar
  9. 53.
    P. Harmand, D. Werner, D. Werner, M-Ideals in Banach Spaces and Banach Algebras. Lecture Notes in Mathematics, vol. 1547 (Springer, Berlin, 1993)CrossRefGoogle Scholar
  10. 79.
    Å. Lima, Intersection properties of balls in spaces of compact operators. Ann. Inst. Fourier (Grenoble) 28, 35–65 (1978)MathSciNetCrossRefGoogle Scholar
  11. 80.
    J. Lindenstrauss, Extension of Compact Operators. Memoirs of the American Mathematical Society, vol. 48 (American Mathematical Society, Providence, RI, 1964)MathSciNetCrossRefGoogle Scholar
  12. 83.
    G. López, M. Martín, R. Payá, Real Banach spaces with numerical index 1. Bull. Lond. Math. Soc. 31, 207–212 (1999)MathSciNetCrossRefGoogle Scholar
  13. 96.
    M. Martín, R. Payá, On CL-spaces and almost-CL-spaces. Ark. Mat. 42, 107–118 (2004)MathSciNetCrossRefGoogle Scholar
  14. 113.
    M. Sharir, Extremal structure in operator spaces. Trans. Am. Math. Soc. 186, 91–111 (1973)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