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Some Reminders of Functional Analysis

  • Bernard Aupetit
Part of the Universitext book series (UTX)

Abstract

This short chapter is intended as an aide-mémoire of some fundamental results in functional analysis that will be used in the rest of this book. Consequently we shall give no proofs as they can be easily found in all the standard textbooks (for instance [7], [8]), with two exceptions: the proof of Milman’s theorem (Theorem 1.1.12) and the nice and simple proof of Machado’s theorem (Theorem 1.1.16) which is a strong extension of the Stone-Weierstrass theorem.

Keywords

Banach Space Probability Measure Extreme Point Convex Space Compact Convex Subset 
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-Verlag New York, Inc. 1991

Authors and Affiliations

  • Bernard Aupetit
    • 1
  1. 1.Départment de Mathématiques et StatistiqueUniversité LavalQuébecCanada

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