# Adjoint Operator and Subspaces of Hilbert Spaces

Let $H_1$ , $H_2$ Hilbert Spaces with $T:H_1 \to H_2$ adjoint operator and $M_1 < H_1$ , $M_2 < H_2$ their subspaces. Show that:

$T(M_1) \subset M_2$ if, and only if, $T^*({M_2}^{\perp}) \subset {M_1}^{\perp}$