2 problems

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Amenability characterized by non-Hausdorff first cohomology
Let $G$ be an infinite, finitely generated group. Let $M$ be a Banach space with norm $||\ ||_M$ that is also a left $\C G$ -module, and suppose that $G$ acts on $M$ by continuous…
Conjectureopenamenability banach-modules group-cohomologyarXiv posted 2 days ago
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Conjecture that $(p,p)$ -amenability implies amenability
Amenability conjecture. Any $(p,p)$ -amenable locally compact group is amenable.
Conjectureopenamenability banach-modules group-algebrasarXiv posted 2 days ago

Amenability characterized by non-Hausdorff first cohomology