Weak precompactness in projective tensor products

2023/05/10 by Rodríguez, José, Zoca, Abraham Rueda · 1 citation
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2305.06089

Abstract

We give a sufficient condition for a pair of Banach spaces (X,Y) to have the following property: whenever W₁ ⊆ X and W₂ ⊆ Y are sets such that \x⊗ y: x∈ W₁, y∈ W₂\ is weakly precompact in the projective tensor product X \widehat⊗_πY, then either W₁ or W₂ is relatively norm compact. For instance, such a property holds for the pair (ℓ_p,ℓ_q) if 1

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• Gelfand-Phillips-type properties in Banach lattices

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