Compact Operators

  • Francis Hirsch
  • Gilles Lacombe
Part of the Graduate Texts in Mathematics book series (GTM, volume 192)

Abstract

Consider two normed spaces E and F over the same field K = ℝ or ℂ. As usual, we denote by L(E,F) the space of continuous linear maps from E to F,and use the same notation ∥ · ∥ for the norm in E, in F,and in L(E,F). Thus, if TL(E,F), we have \(\left\| T \right\| = \sup \left\{ {\left\| {Tx} \right\|:x \in E with\left\| x \right\| \leqslant 1} \right\}. \)

Keywords

Radon Bini 

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Copyright information

© Springer Science+Business Media New York 1999

Authors and Affiliations

  • Francis Hirsch
    • 1
  • Gilles Lacombe
    • 1
  1. 1.Département de MathématiquesUniversité d’Évry-Val d’EssonneÉvry CedexFrance

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