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

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arxiv 1110.4918 v3 pith:R66QVBJV submitted 2011-10-21 math.OA

Stephen Avsec This is my paper
classification math.OA
keywords algebrasq-gaussianestablishapproximationccapcompletelycontractivegenerators
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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).

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Cited by 2 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score.

  1. Simplicity of q-Gaussian C*-algebras

    math.OA 2026-06 unverdicted novelty 6.0 of 10

    q-Gaussian C*-algebras for |q|<1 are shown to satisfy the Dixmier averaging property and therefore are simple with a unique trace, via rapid decay and spectral gap estimates from free probability.

  2. Curvature, Dolbeault-Dirac operators, and an $\mathrm{L}^p$-index theorem on compact K\"ahler manifolds

    math.FA 2024-01 unverdicted novelty 6.0 of 10

    Proves L^p-index theorem for Dolbeault-Dirac operators on compact Kähler manifolds with index equal to holomorphic Euler characteristic χ(M,E) independent of p, using new abstract curvature bound for semigroups.

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