The separation property is a concept in the study of von Neumann algebras that describes a specific condition regarding the representation of states and their associated vectors. This property indicates that a vector is separating if it allows for the identification of states in the algebra by ensuring that distinct states can be distinguished through their inner products. In simpler terms, it helps to separate out different elements in a mathematical structure, making it essential for understanding cyclic and separating vectors within the context of operator algebras.
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