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These notes are dedicated to the study of the complexity of several classes of separable Banach spaces. We compute the complexity of the Banach-Saks property, the alternating Banach-Saks property, the complete continuous property, and the LUST property. We also show that the weak Banach-Saks property, the Schur property, the Dunford-Pettis property, the analytic Radon-Nikodym property, the set of Banach spaces whose set of unconditionally converging operators is complemented in its bounded operators,...
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