About: Cyclic and separating vector

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In mathematics, the notion of a cyclic and separating vector is important in the theory of von Neumann algebras, and in particular in Tomita–Takesaki theory. A related notion is that of a vector which is cyclic for a given operator. The existence of cyclic vectors is guaranteed by the Gelfand–Naimark–Segal (GNS) construction.

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  • In mathematics, the notion of a cyclic and separating vector is important in the theory of von Neumann algebras, and in particular in Tomita–Takesaki theory. A related notion is that of a vector which is cyclic for a given operator. The existence of cyclic vectors is guaranteed by the Gelfand–Naimark–Segal (GNS) construction. (en)
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  • In mathematics, the notion of a cyclic and separating vector is important in the theory of von Neumann algebras, and in particular in Tomita–Takesaki theory. A related notion is that of a vector which is cyclic for a given operator. The existence of cyclic vectors is guaranteed by the Gelfand–Naimark–Segal (GNS) construction. (en)
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  • Cyclic and separating vector (en)
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