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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 Johan.
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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 6905 times total.

Classification:
AMS MSC: 46C99 (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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