# Weak* operator topology and finite rank operators

We will say that ${T_i}\subset B(X,Y^*)$ converges to $T$ in W*-operator topology if $T_i(x)\rightarrow T(x)$ in W*-topology of $Y^*$( $\forall y\in Y \langle T_i(x),y\rangle \rightarrow \langle T(x),y\rangle$).

Now someone has proved the below theorem. Is it true?

BEGIN

Let $X$ and $Y$ be two arbitrary Banach spaces. Then $F (X; Y^*)$(Finite rank operator) is dense in $B(X; Y^*)$ with respect to the weak* operator topology.

Proof.