  We extend some results about sampling of entire functions of exponential type
to Banach spaces. By using generator $D$ of one-parameter group $e^{tD}$ of
isometries of a Banach space $E$ we introduce Bernstein subspaces
$\mathbf{B}_{\sigma}(D),\>\>\sigma>0,$ of vectors $f$ in $E$ for which
trajectories $e^{tD}f$ are abstract-valued functions of exponential type which
are bounded on the real line. This property allows to reduce sampling problems
for $e^{tD}f$ with $f\in \mathbf{B}_{\sigma}(D)$ to known sampling results for
regular functions of exponential type $\sigma$.
