Operator spaces and Araki-Woods factors --A quantum probabilistic approach--

2005/04/12 by Marius Junge, Junge, Marius
Mathematics · #46L53 #47L25 #Advanced Banach Space Theory #Advanced Operator Algebra Research #FOS: Mathematics #Functional Analysis (math.FA) #Operator Algebras (math.OA) #Random Matrices and Applications

paper · pdf · doi:10.48550/arxiv.math/0504255

openalex publication_date 2005/04/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show that the operator Hilbert space OH introduced by Pisier embeds into the predual of the hyerfinite III1 factor. The main new tool is a Khintchine type inequality for the generators of the CAR algebra with respect to a quasi-free state. Our approach yields a Khintchine type inequality for the q-gaussian variables for all values q between -1 and 1. These results are closely related to recent results of Pisier and Shlyakhtenko in the free case.

Citations

• Banach embedding properties of non-commutative L^p-spaces
• A quantum-mechanical central limit theorem

Related

• Hilbert space-valued Gaussian processes, and quantum states
• Fullness of q-Araki-Woods factors
• Quantum inequalities and their applications
• Self-adjoint Operators as Functions II: Quantum Probability
• Bistochastic operators and quantum random variables