Lie Groups pp 17-20 | Cite as

Compact Operators

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


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.


Hilbert Space Orthonormal Basis Compact Operator Compact Space Convergent Subsequence 


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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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