Summary
In this paper certain translation invariant states on the infinite tensor productC *-algebra
are considered. Form ∈ ℤ+ a state ϕ onA ism-dependent if
wheneverl>k+m anda k + 1 =a k + 2 = ... =a k +m = 1. The closed convex hull of the stationarym-dependent states is characterized by a symmetry condition. The case ofm=0 corresponds to independence and the result reduces to aC *-algebraic version, due to E. Størmer, of the classical de Finetti's theorem on exchangeable sequences.
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Partially supported by the Hungarian National Foundations for Scientific Research grant no. 1816. On leave of absence from the Mathematical Institute HAS, Budapest
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Petz, D. A de Finetti-type theorem withm-dependent states. Probab. Th. Rel. Fields 85, 65–72 (1990). https://doi.org/10.1007/BF01377629
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DOI: https://doi.org/10.1007/BF01377629