科研之友
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摘要
Bounded observables corresponding to a quantum system are usually represented by S(H), the set of all bounded linear self-adjoint operators on a Hilbert space H. In 2006, Gudder introduced a logic order, , on S(H). For A,B is an element of S(H), AB if and only if there exists C is an element of S(H) such that AC=0 and A C=B. Given A,B is an element of S(H), let AB be the least upper bound (supremum) for A and B with respect to the Gudder order. In 2007, Pulmannova and Vincenkova proved that AB exists if and only if A and B have an upper bound for the Gudder order. In this paper, we present some new necessary and sufficient conditions for which AB exists and give an explicit representation of AB (if AB exists).
