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.
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References for Chapter HI
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].
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© 1978 Springer-Verlag Berlin Heidelberg
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Yosida, K. (1978). The Orthogonal Projection and F. Riesz’ Representation Theorem. In: Functional Analysis. Grundlehren der mathematischen Wissenschaften, vol 123. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-96439-8_4
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DOI: https://doi.org/10.1007/978-3-642-96439-8_4
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-96441-1
Online ISBN: 978-3-642-96439-8
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