Strong Solidity of the q-Gaussian Algebras for all -1 < q < 1

Abstract

The main result of this paper is to establish the weak* completely contractive approximation property (w*CCAP) for the q-Gaussian algebras for all values of q \in [-1, 1] and any number of generators. We use this to establish that the q-Gaussian algebras are strongly solid in the sense of Popa and Ozawa for q \in (-1, 1).

35 pages, 8 figures, significant changes made mainly to the third and fourth sections

References in corpus (3)

• Examples of groups which are not weakly amenable
• Non injectivity of the q-deformed von Neumann algebra
• Strong solidity of group factors from lattices in SO(n,1) and SU(n,1)

Cited by in corpus (5)

• Complete metric approximation property for $q$-Araki-Woods algebras
• $L_2$-cohomology, derivations and quantum Markov semi-groups on $q$-Gaussian algebras
• Singularity of the generator subalgebra in $q$-Gaussian algebras
• On the classification and modular extendability of E${}_0$-semigroups on factors
• Maximal amenability of the generator subalgebra in $q$-Gaussian von Neumann algebras