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Completeness of Inner Product Spaces Induced by States on Jordan and C -Algebras

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We show that a state φ on a Jordan algebra 𝓐 induces complete inner product space if and only if φ is a convex combination of pure states. Inner product spaces generated by Type I n factor states and states on spin factors are described. We initiate study of completely positive maps in this connection by showing that pure completely positive map on a C -algebra gives always complete inner product space in the Stinespring construction.

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Correspondence to Ekaterina Turilova.

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Turilova, E. Completeness of Inner Product Spaces Induced by States on Jordan and C -Algebras. Int J Theor Phys 54, 4229–4236 (2015).

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