The Hahn–Banach Theorems

  • Adam BowersEmail author
  • Nigel J. Kalton (deceased)
Part of the Universitext book series (UTX)


Several theorems in functional analysis have been labeled as “the Hahn–Banach Theorem.” At the heart of all of them is what we call here the Hahn–Banach Extension Theorem, given in Theorem 3.4, below. This theorem is at the foundation of modern functional analysis, and its use is so pervasive that its importance cannot be overstated.


Hahn-Banach Extension Theorem Modern Functional Analysis Sublinear Functionals Hausdorff Maximal Principle Orthogonal Operator 
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Copyright information

© Springer Science+Business Media, LLC 2014

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of California, San DiegoLa JollaUSA
  2. 2.Department of MathematicsUniversity of Missouri, ColumbiaColumbiaUSA

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