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Riesz representation theorem (Theorem)

For every continuous linear functional $f$ on a Hilbert space $\mathcal{H}$ , there is a unique $u\in \mathcal{H}$ such that $f(x)=\langle x,u \rangle$ for all $x\in\mathcal{H}$ .
Note: $\langle x,u \rangle$ denotes the inner product between $x$ and $u$ .




"Riesz representation theorem" is owned by azdbacks4234. [ owner history (1) ]
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See Also: Riesz-Fischer theorem


Attachments:
proof of Riesz representation theorem for separable Hilbert spaces (Proof) by asteroid
proof of Riesz representation theorem (Proof) by asteroid
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Cross-references: inner product, Hilbert space, linear functional, continuous
There are 8 references to this entry.

This is version 6 of Riesz representation theorem, born on 2004-02-16, modified 2004-02-17.
Object id is 5585, canonical name is RieszRepresentationTheorem.
Accessed 8910 times total.

Classification:
AMS MSC46C99 (Functional analysis :: Inner product spaces and their generalizations, Hilbert spaces :: Miscellaneous)

Pending Errata and Addenda
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another or extended version by igor on 2004-02-17 01:34:50
Isn't there another version of this theorem which states that
each linear functional on the space of functions (which space?)
on a set X equivalent to a measure on X, and vice versa?
Or am I completely off the mark here?

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