Let H be a Hilbertspace, H' the Dualspace of H.

We know from Riesz representation theorem that for every $\phi \in H'$ there is exaclty one $y \in H$ such that

$\phi(x) = \langle x,y \rangle$ for every $x \in H$.

Now is it also possible that for a $\phi \in H'$ we find exactly one $y \in H$ such that

$f(y) = \langle f, \phi \rangle$ for every $f \in H'$ ?

If so, how does that follow from Riesz representation theorem?


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