The Orthogonal Projection and F. Riesz’ Representation Theorem

  • Kôsaku Yosida
Part of the 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 spades is founded on this theorem.




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References for Chapter HI

  1. For general account of Hilbert spaces, see N. I. Achieser-I. M. Glasman [1], N. Dunford-J. Schwartz [2], B. Sz. Nagy [1], F. Riesz-B. Sz. Nagy [3] and M. H. Stone [1].Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1978

Authors and Affiliations

  • Kôsaku Yosida
    • 1
  1. 1.Kamakura, 247Japan

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