The Orthogonal Projection and F. Riesz’ Representation Theorem
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 , and the whole theory of Hilbert spaces is founded on this theorem.
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