A non-commutative random stopping theorem

Abstract

A theory of non-commutative stopping time is presented in the case where the underlying Von Neumann algebra possesses only a faithful normal state. In particular we prove an analogue of Doob's optional stopping theorem and in the special case of the quasi-free representation of the CAR we are also able to prove the random stopping theorem. These results thus extend those established by C. Barnett and T. J. Lyons (1985, Math. Proc. Cambridge Philos. Soc.) to include certain type III factors.