Analysis Seminar: "Noncommutative martingales in product settings"
Abstract: We revisit Miguel de Guzmán's proof of the strong maximal theorem and we give an argument that can be generalized to noncommutative probability spaces (i.e. to von Neumann algebras with finite trace). The main difficulty that we must face is the definition of the operator itself: in principle, one cannot make sense of the supremum of a sequence of positive operators, something that can be done pointwise for a sequence of functions.
Host: Francesco Di Plinio