Norm of the algebraic adjoint of a bounded linear operator in Hilbert space

Question

Let $H,K$ be Hilbert spaces. Let $F : H \rightarrow K$.

I want to show that $\|F^T \|= \| F\|$, where $F^T$ is the algebraic adjoint.

I have that $\| F\|= \sup \{ | \langle Fx,x \rangle| : x\in H, \| x\|=1\}$, and $\| F\| = \| F^*\|$.

However, I'm not sure how to using the information above to show $\|F^T \|= \| F\|$.

Any hints or ideas will be appreciated!

Thanks!