0
$\begingroup$

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?

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Browse other questions tagged or ask your own question.