hal-00077597, version 1
Non injectivity of the q-deformed von Neumann algebra
Mathematische Annalen 330 number 1 (2004) 17-38
Abstract: We prove that the von Neumann algebra generated by q-gaussians is not injective as soon as the dimension of the underlying Hilbert space is greater than 1. Our approach is based on a vector valued Khintchine type inequality for Wick products. The same proof also works for the more general setting of a Yang-Baxter deformation. Our techniques can also be extended to the so called q-Araki-Woods von Neumann algebras recently introduced by Hiai. In this latter case, we obtain the non injectivity under some asssumption on the spectral set of the positive operator associated with the deformation.
- 1:
- Université d'Orléans – CNRS : UMR7349
- 2:
- CNRS : UMR6623 – Université de Franche-Comté
- Domain : Mathematics/Operator Algebras
- Keywords : injectivity – Gaussian – deformation – Yang-Baxter Operator
- hal-00077597, version 1
- http://hal.archives-ouvertes.fr/hal-00077597
- oai:hal.archives-ouvertes.fr:hal-00077597
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- Submitted on: Wednesday, 31 May 2006 13:41:09
- Updated on: Tuesday, 6 June 2006 18:02:31
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