Proving a variant of closed range theorem on Hilbert space

I've been working on closed range theorem. There are a lot of materials on general Banach spaces, but not much on Hilbert spaces, so I was wondering if I could get some help.I'm trying to prove the following claim:

A bounded linear map $T:X\to Y$ between Hilbert spaces $X$ and $Y$ has closed range if and only if there exists a constant $C>0$ so that $\|f\| \le C\|T^*f\|$

This statement seems like the statement is a usual closed range theorem, but a bit different, especially with adjoint of the operator. Can someone help me proving this claim? Thanks!