Examples of groups which are not weakly amenable

By Nathanial P. Brown Narutaka Ozawa. 2010

84 citations recorded by the source corpus.

We prove that weak amenability of a locally compact group imposes a strong condition on its amenable closed normal subgroups. This extends non weak amenability results of Haagerup (1988) and Ozawa--Popa (2010). A von Neumann algebra analogue is also obtained.

Subfields: Algebra and Number Theory, Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/135a1021ab2b954a66357150eac78a42f7506574

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In Algebra and Number Theory

1. Gilles Pisier
2. I. Chifan
3. Bogdan Udrea
4. Uffe Haagerup
5. Thomas Sinclair
6. Adrian Ioana
7. S. Vaes
8. 'Eric Ricard

In Applied Mathematics

1. Gilles Pisier
2. I. Chifan
3. Thomas Sinclair
4. Uffe Haagerup
5. Bogdan Udrea
6. Assaf Naor
7. Benben Liao
8. Cyril Houdayer

In Mathematical Physics

1. Gilles Pisier
2. I. Chifan
3. Bogdan Udrea
4. Thomas Sinclair
5. Uffe Haagerup
6. Adrian Ioana
7. Roland Speicher
8. Marius Junge

Citations in the corpus

• Unique Cartan decomposition for II_1 factors arising from arbitrary actions of hyperbolic groups (2012, unknown): “k form of malleable deformation from the coarse cocycle, then applying it to the almost invariance property resulting from the weak compactness of arbitrary Cartan subalgebras of L∞(X)⋊Γ, obtained in [Oz10]. In this way, [CS11] succeeded in proving that the group measure space II1 factor L∞(X)⋊Γ ass”
• Tensor Products of C*-Algebras and Operator Spaces (2020, background): “Haagerup (1986, unpublished) proved that SL3(Z) is not weakly amenable (see also [190]), even though C∗ λ(G) is exact when G = SL3(Z) as well as when G is any closed discrete subgroup of a connected Lie group.”
• Group C*-Algebras without the Completely Bounded Approximation Property (2016, result): “orofaeff, Seeger, and Wright [CDSW05] extended the previous results to cover many non-simple Lie groups including all real algebraic linear groups. In 2012, Ozawa gave a short proof of Theorem 1 (see [Oza12] and [Knu15]). In 1994, a weaker approximation property (called the Approximation Property or”
• Examples of factors which have no Cartan subalgebras (2012, unknown): “Theorem 4.1.1 ([24], [22]) .”
• ON THE STRUCTURAL THEORY OF II1 FACTORS OF NEGATIVELY CURVED GROUPS, II. ACTIONS BY PRODUCT GROUPS (2011, methodology): “En devéloppant une nouvelle approche, qui combine les méthodes de Peterson [29], d’Ozawa et Popa [27, 28], et d’Ozawa [25], nous renforçons ce résultat en montrant que ce facteur est fortement solide.”