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The Orthogonal Projection and F. Riesz’ Representation Theorem

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

Abstract

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.

Keywords

Hilbert Space Orthogonal Projection Dual Space Representation Theorem Normed Linear Space 
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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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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