Unconditional Schauder decompositions and stopping times in the Lebesgue–Bochner spaces

Abstract

We extend Troitsky's study of martingales in Banach lattices to include stopping times. Results from the theory of unconditional Schauder decompositions and multipliers are used to derive an optional stopping theorem for unbounded stopping times. We also apply these techniques to convergent nets of stopped processes, as well as to unconditional Schauder decompositions in vector-valued L p -spaces ( 1 < p < ∞ ).