Let $\displaystyle H$ be a Hilbert space. Show that $\displaystyle H^* $ is also a Hilbert space with respect to the inner product defined by $\displaystyle (f_x,f_y) = (y,x)$.

($\displaystyle x,y \in H , f_y,f_x \in H^*$ )

I had proven that it is an inner product space and my problem is how to show that $\displaystyle H^*$ is a Hilbert space.

Can anyone help?