SOME RESULTS ON BZ STRUCTURES FROM HILBERTIAN UNSHARP QUANTUM PHYSICS

Some algebraic structures determined by the class Sigma(H) of all effects of a Hilbert space H and by some subclasses of Sigma(H) are investigated in particular de Morgan-Brouwer-Zadeh posers [it is proved that Sigma(H-n) (n < infinity) has such a structure], Brouwer-Zadeh* posets (a quite trivial example consisting of suitable effects is given), and Brouwer-Zadeh(3) posers which are both de Morgan and *. It is shown that a nontrivial class of effects of a Hilbert space exists which is a BZ(3) poser. All epsilon-preclusivity relation on the set of all vectors of H is introduced, and it is shown that it satisfies the regularity condition also for epsilon epsilon [1/2, 1].