Abstract
Publisher Summary This chapter describes the spaces of quantum observables. The quantum observables are identified with the self-adjoint linear operators acting on some separable Hilbert space. Mathematical structures on a set of observables are defined in this chapter. The quantum states can be identified with the self-adjoint, nonnegative linear operators ρ of unit trace. The density operators represent states in quantum mechanics. A set of quantum observables can be a Hilbert space. It is suggested that an operator Hilbert space is a complete pre-Hilbert operator space.
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