Spear Operators Between Banach Spaces

  • Vladimir Kadets
  • Miguel Martín
  • Javier Merí
  • Antonio Pérez

Part of the Lecture Notes in Mathematics book series (LNM, volume 2205)

Table of contents

  1. Front Matter
    Pages i-xv
  2. Vladimir Kadets, Miguel Martín, Javier Merí, Antonio Pérez
    Pages 1-36
  3. Vladimir Kadets, Miguel Martín, Javier Merí, Antonio Pérez
    Pages 37-47
  4. Vladimir Kadets, Miguel Martín, Javier Merí, Antonio Pérez
    Pages 49-66
  5. Vladimir Kadets, Miguel Martín, Javier Merí, Antonio Pérez
    Pages 67-82
  6. Vladimir Kadets, Miguel Martín, Javier Merí, Antonio Pérez
    Pages 83-95
  7. Vladimir Kadets, Miguel Martín, Javier Merí, Antonio Pérez
    Pages 97-102
  8. Vladimir Kadets, Miguel Martín, Javier Merí, Antonio Pérez
    Pages 103-113
  9. Vladimir Kadets, Miguel Martín, Javier Merí, Antonio Pérez
    Pages 115-150
  10. Vladimir Kadets, Miguel Martín, Javier Merí, Antonio Pérez
    Pages 151-152
  11. Back Matter
    Pages 153-164

About this book

Introduction

This monograph is devoted to the study of spear operators, that is, bounded linear operators $G$ between Banach spaces $X$ and $Y$ satisfying that for every other bounded linear operator $T:X\longrightarrow Y$ there exists a modulus-one scalar $\omega$ such that
$\|G + \omega\,T\|=1+ \|T\|$.

This concept extends the properties of the identity operator in those Banach spaces having numerical index one. Many examples among classical spaces are provided, being one of them the Fourier transform on $L_1$. The relationships with the Radon-Nikodým property, with Asplund spaces and with the duality, and some isometric and isomorphic consequences are provided. Finally, Lipschitz operators satisfying the Lipschitz version of the equation above are studied.
 
The book could be of interest to young researchers and specialists in functional analysis, in particular to those interested in Banach spaces and their geometry. It is essentially self-contained and only basic knowledge of functional analysis is needed.

Keywords

Banach Space Bounded Linear Operator Daugavet Equation Daugavet Property, Alternative Daugavet Property Numerical Range of Operators Numerical Index of Banach Spaces Lush Space Spear Operator Lipschitz Operator

Authors and affiliations

  • Vladimir Kadets
    • 1
  • Miguel Martín
    • 2
  • Javier Merí
    • 3
  • Antonio Pérez
    • 4
  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 Análisis MatemáticoUniversidad de GranadaGranadaSpain
  4. 4.Departamento de MatemáticasUniversidad de MurciaMurciaSpain

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-71333-5
  • Copyright Information Springer International Publishing AG, part of Springer Nature 2018
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-71332-8
  • Online ISBN 978-3-319-71333-5
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • About this book
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