科研之友
微信
新浪微博
Facebook
分享链接
摘要
The set of bounded observables for a quantum system is represented by the set of bounded self-adjoint operators S(H) on a complex Hilbert space H, and the quantum effects for a physical system can be described by the set E(H) of positive contractive operators on a complex Hilbert space H. In this note, by the techniques of operator block and spectral, we give the simpler representation of A boolean AND P and obtained the new necessary and sufficient conditions for A boolean OR P, for A is an element of S(H) and P is an element of P(H), where P(H) is the set of all orthogonal projection operators on H. In particular, we get that if A boolean OR P exists, then A boolean OR P is an element of E(H) for A is an element of E(H) and P is an element of P(H). In addition, we consider the relations between the existence of A boolean OR B, A(-)boolean OR B-, and A(+)boolean OR B+, where A(+), B+, A(-), and B- are the positive and negative parts of A,B is an element of S(H).
