The Orthogonal Projection and F. Riesz’ Representation Theorem

  • Kôsaku Yosida
Part of the Die Grundlehren der Mathematischen Wissenschaften book series (GL, volume 123)


In a pre-Hilbert space, we can introduce the notion of orthogonality of two vectors. Thanks to this fact, a Hilbert space may be identified with its dual space, i.e., the space of bounded linear functionals. This result is the representation theorem of F. Riesz [1], and the whole theory of Hilbert spaces is founded on this theorem.


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References for Chapter III

  1. For general account of Hilbert spaces, see Achieser, N. I. [1]MATHGoogle Scholar
  2. Nagy, B. von Sz. [1]CrossRefGoogle Scholar
  3. Riesz, F. [3]Google Scholar
  4. Stone, M. H. [1]Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1965

Authors and Affiliations

  • Kôsaku Yosida
    • 1
  1. 1.University of TokyoJapan

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