LATTICE OF TRIPOTENTS IN A JBW-ASTERISK-TRIPLE

The complete lattice of tripotents in a JBW-triple and the unit ball in its predual are respectively proposed as models for the complete la ttice of propositions and for the generalized normal state space of a nonassociative, noncommutative physical system. A subsystem of such a system may be defined in terms of either principal ideals in the compl ete lattice of propositions or norm-closed faces of the generalized st ate space. It is shown that the two definitions are equivalent and tha t each subsystem is associative.