Can anyone help me prove this?
Let $T$ be a linear operator in a Hilbert space $H$ so that $\langle Tx, y \rangle = i\langle x, Ty \rangle$ for all $x, y \in H$. Show that $T$ is bounded.
I think I should use the closed graph theorem, but it is not clear to me how to do it. Any help will be very welcome.