  The translation of an operator is defined by using conjugation with
time-frequency shifts. Thus, one can define $\Lambda$-shift-invariant subspaces
of Hilbert-Schmidt operators, finitely generated, with respect to a lattice
$\Lambda$ in $\mathbb{R}^{2d}$. These spaces can be seen as a generalization of
classical shift-invariant subspaces of square integrable functions. Obtaining
sampling results for these subspaces appears as a natural question that can be
motivated by the problem of channel estimation in wireless communications.
These sampling results are obtained in the light of the frame theory in a
separable Hilbert space.
