let $H$ be a Hilbert space. the space of all operator with finite rank on $H$ is shown by $F ( H ) $.
we know that $ F(H) \subseteq K(H) \subseteq B(H) $ so that $K(H) $ is compact operator on$H$ and $B(H)$ is bounded operator on $H$.
Is it right to say, if $ T \in F( H )$ then $ T^{*} \in F (H)$?