Weakly sequential completeness of the projective tensor product {𝐿^{{}𝑝}[0,1]{̂⊗}𝑋,1<𝑝<∞}

Bu, Qingying

doi:10.1090/S0002-9939-03-07052-7

Weakly sequential completeness of the projective tensor product {$L^\{p\}[0,1]\hat \{\otimes \}X, 1 < p < \infty$}
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Proc. Amer. Math. Soc. 132 (2004), 381-384 Request permission

Abstract:

D. R. Lewis (1977) proved that for a Banach space $X$ and $1 < p < \infty$, $L^p[0,1]\hat {\otimes }X$, the projective tensor product of $L^p[0,1]$ and $X$, is weakly sequentially complete whenever $X$ is weakly sequentially complete. In this note, we give a short proof of Lewis’s result, based on our sequential representation (2001) of $L^p[0,1]\hat {\otimes }X$.

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