English

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

Operator Algebras 2008-06-24 v1

Abstract

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.

Keywords

Cite

@article{arxiv.0806.3632,
  title  = {On Lehner's `free' noncommutative analogue of De Finetti's theorem},
  author = {Claus Köstler},
  journal= {arXiv preprint arXiv:0806.3632},
  year   = {2008}
}

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9 pages