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Derivatives in Vector Spaces

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

Abstract

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

    λ is continuous.

     
  2. (2)
    There exists C > 0 such that for all υE we have
    $$\left| {\lambda (\upsilon )} \right| \leqq C\left| \upsilon \right|$$
    .
     

Keywords

Vector Space Partial Derivative Column Vector High Derivative Normed Vector Space 
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 1997

Authors and Affiliations

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

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