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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

We recall the concept of spear vector and introduce the new notion of spear set. They are both used as “leitmotiv” to give a unified presentation of the concepts of spear operator, lush operator, aDP, and other type of operators that will be introduced here. We collect some properties of spear sets and vectors, together with some (easy) examples of spear vectors.

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. XIIIGoogle 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)CrossRefGoogle 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)Google 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)Google 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

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