On the Order Structure of Time Projection

The order structure of time projections associated with random times in a von Neumann algebra is investigated in the general setup as well as that of the CAR and CCR algebras. In the second case various additional properties (such as e.g. the upper/lower continuity) of the lattice of time projections are also discussed. 0. Introduction In this paper we investigate the order structure of time projections associated with random times in an arbitrary non-commutative filtration of a von Neumann algebra as well as those employed in quantum stochastic theory of the canonical anticommutation relations (CAR) and the canonical commutation relations (CCR) (cf. [4], [9]). Within the context of certain quasi-free representations of the CAR and CCR, we give an answer to a question posed in [3] — the dual of Theorem 1.12 of [3] (see Theorem 2.7 and Theorem 3.5 in this paper, which can be considered as a partial answer to that question for an arbitrary non-commutative filtration). 2000 Mathematics Subject Classification. Primary: 46L53; Secondary: 81S25.