Derivatives in Vector Spaces

  • Serge Lang
Part of the Undergraduate Texts in Mathematics book series (UTM)


Let E, F be normed vector spaces. Let λ: E → F be a linear map. The following two conditions on λ are equivalent:
  1. (1)

    λ is continuous.

  2. (2)
    Three exists C > 0 such that for all y e E we have
    $$\left| {\lambda \left( v \right)} \right|\underline{\underline < } C\left| v \right|.$$


Vector Space Partial Derivative Column Vector Coordinate Function High Derivative 
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 1983

Authors and Affiliations

  • Serge Lang
    • 1
  1. 1.Department of MathematicsYale UniversityNew HavenUSA

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