Normed linear spaces

  • Arlen Brown
  • Carl Pearcy
Part of the Graduate Texts in Mathematics book series (GTM, volume 55)


We here commence our study of the fundamentals of the branch of mathematics known as functional analysis. In the course of this study and, indeed, throughout the balance of this book, we shall constantly be dealing with various linear spaces that are at the same time equipped with a topology. Frequently the topology will be induced by a metric. In this connection the following concept is useful.


Banach Space Linear Space Normed Space Topological Vector Space Normed Linear Space 


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Copyright information

© Springer-Verlag, New York Inc. 1977

Authors and Affiliations

  • Arlen Brown
    • 1
  • Carl Pearcy
    • 2
  1. 1.Department of MathematicsIndiana UniversityBloomingtonUSA
  2. 2.Department of MathematicsUniversity of MichiganAnn ArborUSA

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