The von Neumann algebras generated by t -gaussians

Éric Ricard[1]

  • [1] Laboratoire de Mathématiques Université de Franche-Comté 25030 Besançon, cedex (France)

Annales de l’institut Fourier (2006)

  • Volume: 56, Issue: 2, page 475-498
  • ISSN: 0373-0956

Abstract

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We study the t -deformation of gaussian von Neumann algebras. They appear as example in the theories of Interacting Fock spaces and conditionally free products. When the number of generators is fixed, it is proved that if t is sufficiently close to 1 , then these algebras do not depend on t . In the same way, the notion of conditionally free von Neumann algebras often coincides with freeness.

How to cite

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Ricard, Éric. "The von Neumann algebras generated by $t$-gaussians." Annales de l’institut Fourier 56.2 (2006): 475-498. <http://eudml.org/doc/10154>.

@article{Ricard2006,
abstract = {We study the $t$-deformation of gaussian von Neumann algebras. They appear as example in the theories of Interacting Fock spaces and conditionally free products. When the number of generators is fixed, it is proved that if $t$ is sufficiently close to $1$, then these algebras do not depend on $t$. In the same way, the notion of conditionally free von Neumann algebras often coincides with freeness.},
affiliation = {Laboratoire de Mathématiques Université de Franche-Comté 25030 Besançon, cedex (France)},
author = {Ricard, Éric},
journal = {Annales de l’institut Fourier},
keywords = {Conditionnal free product; interacting Fock space; t-Gaussians; generated von Neumann algebra; t-deformed Fock space; orthogonal polynomials; conditional free product; R and G transforms},
language = {eng},
number = {2},
pages = {475-498},
publisher = {Association des Annales de l’institut Fourier},
title = {The von Neumann algebras generated by $t$-gaussians},
url = {http://eudml.org/doc/10154},
volume = {56},
year = {2006},
}

TY - JOUR
AU - Ricard, Éric
TI - The von Neumann algebras generated by $t$-gaussians
JO - Annales de l’institut Fourier
PY - 2006
PB - Association des Annales de l’institut Fourier
VL - 56
IS - 2
SP - 475
EP - 498
AB - We study the $t$-deformation of gaussian von Neumann algebras. They appear as example in the theories of Interacting Fock spaces and conditionally free products. When the number of generators is fixed, it is proved that if $t$ is sufficiently close to $1$, then these algebras do not depend on $t$. In the same way, the notion of conditionally free von Neumann algebras often coincides with freeness.
LA - eng
KW - Conditionnal free product; interacting Fock space; t-Gaussians; generated von Neumann algebra; t-deformed Fock space; orthogonal polynomials; conditional free product; R and G transforms
UR - http://eudml.org/doc/10154
ER -

References

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  16. D. V. Voiculescu, K. J. Dykema, A. Nica, Free random variables, 1 (1992), American Mathematical Society, Providence, RI Zbl0795.46049MR1217253
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