Factoriality of q-Gaussian von Neumann Algebras

By 'Eric Ricard. 2003

76 citations recorded by the source corpus.

We prove that the von Neumann algebras generated by nq-Gaussian elements, are factors for n≥2.

Subfields: Algebra and Number Theory, Mathematical Physics, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/92d68e0b5df77c00f0d61f301002af9b0eed2012

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In Algebra and Number Theory

1. Quanhua Xu
2. Marius Junge
3. Nathanial P. Brown Narutaka Ozawa
4. Gilles Pisier
5. Adrian Ioana
6. W. Winter
7. Thomas Sinclair
8. Amaury Freslon

In Mathematical Physics

1. Marius Junge
2. Quanhua Xu
3. Nathanial P. Brown Narutaka Ozawa
4. Narcisse Randrianantoanina
5. Gilles Pisier
6. Tao Mei
7. Javier Parcet
8. Sjoerd Dirksen

In Statistics and Probability

1. Marius Junge
2. Quanhua Xu
3. Nathanial P. Brown Narutaka Ozawa
4. Narcisse Randrianantoanina
5. Javier Parcet
6. Sjoerd Dirksen
7. Tao Mei
8. Joel A. Tropp

Citations in the corpus

• A Kurosh-type theorem for type II1 factors (2004, background): “Indeed, solidity for certain values of q was proved by Shlyakhtenko [Sh] while factoriality for all values of q was proved by Ricard [Ri].”
• Noncommutative maximal ergodic theorems (2005, background): “Hence q(HR) is a type II1 von Neumann algebra for q [N ] and [Ri] for more information.”