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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

Hilbert Space Compact Operator Selfadjoint Operator Nonzero Eigenvalue Finite Rank 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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