Abstract:We study the property of being strongly weakly compactly generated (and some relatives) in projective tensor products of Banach spaces. Our main result is as follows. Let $1 < p,q<\infty$ be such that $1/p+1/q\geq 1$. Let X (resp., Y) be a Banach space with a countable unconditional finite-dimensional Schauder decomposition having a disjoint lower p-estimate (resp., q-estimate). If X and Y are strongly weakly compactly generated, then so is their projective tensor product $X {\widehat{\ot… Show more
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