  Monotone convex operators and time-consistent systems of operators appear
naturally in stochastic optimization and mathematical finance in the context of
pricing and risk measurement. We study the dual representation of a monotone
convex \emph{operator} when its domain is defined on a subspace of $L_p$, with
$p\in [1,\infty]$, and we prove a sandwich preserving extension theorem. These
results are then applied to study systems of such operators defined only on
subspaces. We propose various dynamic sandwich preserving extension results
depending on the nature of time: finite discrete, countable discrete, and
continuous. Of particular notice is the fact that the extensions obtained are
time-consistent.
