Let $T$ be a bounded operator such that $<Tf,f>=0$ then $T=0?$

Question

Let $H$ be a hilbert space. Let $T:H\to H$ be a linear bounded operator such that $<Tf,f>=0$ for all $f\in H$. It is necesarily true that $Tf=0 ?$

When I mean Hilbert space over a field $\mathbb K$ I consider only $\mathbb K= \mathbb C$ or $\mathbb K= \mathbb R$