Suppose that $T$ is a linear operator from a normed linear space $ X $ into normed linear space $ Y $.Prove that the following are equivalent.
$1)$ The operator $T$ is continuous.
$2)$The set $ T(K)$ is a weakly compact subset of $Y$ whenever $K$ is a weakly compact subset of $X$.
1) to 2) is clear but 2) to 1)??