Bilinear maps on Hilbert spaces

Question

Is there any characterization of continuous bilinear maps $m:H_1\times H_2\to \mathbb C$ , where $H_1,H_2$ are Hilbert spaces? I have read somewhere that such bilinear maps are of kind $m(a,b)=\left< Ta,b\right>$ for some $T\in B(H_1,H_2)$ but it looks like to me a sesquilinear form. I am confused.