  In an $L_\infty$-framework, we present a few extension theorems for linear
operators. We focus the attention on majorant preserving and sandwich
preserving types of extensions. These results are then applied to the study of
price systems derived by a reasonable restriction of the class of equivalent
martingale measures applicable. First we consider equivalent martingale
measures with bounds on densities and the corresponding prices bounded by
linear minorant and majorant. Then we consider prices bounded by bid-ask
dynamics. Finally we study price systems consistent with no-good-deal pricing
measures for given bounds on the Sharpe ratio. Within this study we introduce
the definition of dynamic no-good-deal pricing measure.
