I want to show that if a (not necessarily bounded) linear operator $T$ is defined everywhere on a complex Hilbert space $H$, then its Hilbert-adjoint operator $T^*$ is bounded.
Now given that $T$ may not be a bounded operator, we can't just use the Cauchy-Schwarz Inequality to get a bound for $T^*$. But since we can't assume that $T$ is bounded, is there a way to get a bound on $T^*$?
Edit: I think i have figured out the solution now so we can close this problem .