Lie Groups pp 19-22 | Cite as

Compact Operators

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


If \(\mathfrak{H}\) is a normed vector space, a linear operator \(T: \mathfrak{H} \rightarrow \mathfrak{H}\) is called bounded if there exists a constant C such that \(|Tx| \leqslant C|x|\) for all \(x \in \mathfrak{H}\). In this case, the smallest such C is called the operator norm of T, and is denoted |T|.

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

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

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