Are Unitarizable Groups Amenable?

Gilles Pisier

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Quantitative example of a unitarizable group
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23 months ago
Bruce ▴ 45

In theorem 1.1 (see below) Pisier shows that a quantitative condition on the invertible operator which unitarizes a uniformly bounded implies the amenability of the group.

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Is there a known example of an amenable group which has a uniformly bounded representation pi which is unitarizable where ||S|| ||S^-1|| > |pi|^2?

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