Is this a proper statement for the Dual space of a Hilbert space?
Let $H$ be a Hilbert space. The set of all continuous bounded linear maps, $\mathcal{L}(H,\mathbb{R})$, is called the dual space.
I also am trying to understand Riesz's Theorem
This is what I believe the theorem is saying:
Let $H$ be a Hilbert space and $\varphi\in \mathcal{L}(H,\mathbb{R})$. Then there exists a unique $y\in H$ such that $\varphi(x)=\langle x,y\rangle$ for all $x\in H$.