Electronic Resource
Springer
Probability theory and related fields
85 (1990), S. 65-72
ISSN:
1432-2064
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
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 $$\varphi (a_1 \otimes a_2 \otimes ... \otimes a_l ) = \varphi (a_1 \otimes ... \otimes a_k )\varphi (a_{k + m + 1} \otimes ... \otimes a_l )$$ 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.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01377629
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