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Lie Groups pp 17-20 | Cite as

Compact Operators

  • Daniel Bump
Part of the Graduate Texts in Mathematics book series (GTM, volume 225)

Abstract

If ℌ is a normed linear space, a linear operator T: ℌ → ℌ is called bounded if there exists a constant C such that |Tx| ≤ C|x| for all x ∈ ℌ. In this case, the smallest such C is called the operator norm, of T, and is denoted |T|. The boundedness of the operator T is equivalent to its continuity.

Keywords

Hilbert Space Orthonormal Basis Compact Operator Compact Space Convergent Subsequence 
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 2004

Authors and Affiliations

  • Daniel Bump
    • 1
  1. 1.Department of MathematicsStanford UniversityStanfordUSA

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