Some Examples in Classical Banach Spaces

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


Our aim here is to present examples of operators which are lush, spear, or have the aDP, defined in some classical Banach spaces. One of the most intriguing examples is the Fourier transform on L1, which we prove that is lush. Next, we study a number of examples of operators arriving to spaces of continuous functions. In particular, it is shown that every uniform algebra is lush-embedded into a space of bounded continuous functions. Finally, examples of operators acting from spaces of integrable functions are studied.


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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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