2 problems

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Gournay dimension-zero characterization by invariant exhaustions
Gournay's dimension-zero conjecture. One has
Conjectureopenamenable-groups ell-p-cohomology sofic-groupsarXiv posted 2 days ago
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The characterization of admissible Banach spaces by nontrivial type
Admissibility conjecture. A Banach space is admissible if and only if it has nontrivial type.
Conjectureopenbanach-spaces ell-p-cohomology property-tarXiv posted 2 days ago

Gournay dimension-zero characterization by invariant exhaustions