On Lehner's `free' noncommutative analogue of De Finetti's theorem

Details On Lehner's `free' noncommutative analogue of De Finetti's theorem On Lehner's `free' noncommutative analogue of De Finetti's theorem

2008-06-23

arxiv.org/abs/0806.3632v1

Mathematics

Operator Algebras

9 pages

Scientific paper

Inspired by Lehner's results on exchangeability systems we define `weak conditional freeness' and `conditional freeness' for stationary processes in an operator algebraic framework of noncommutative probability. We show that these two properties are equivalent and thus the process embeds into a von Neumann algebraic amalgamated free product over the fixed point algebra of the stationary process.

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