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Weakly sequential completeness of the projective tensor product $L^{\lowercase{p}}[0,1]\hat{\otimes}X, 1 < \lowercase{p} < \infty$


Author: Qingying Bu
Journal: Proc. Amer. Math. Soc. 132 (2004), 381-384
MSC (2000): Primary 46M05, 46B28, 46E40
DOI: https://doi.org/10.1090/S0002-9939-03-07052-7
Published electronically: June 11, 2003
MathSciNet review: 2022359
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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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Additional Information

Qingying Bu
Affiliation: Department of Mathematics, University of Mississippi, University, Mississippi 38677
Email: qbu@olemiss.edu

DOI: https://doi.org/10.1090/S0002-9939-03-07052-7
Keywords: Projective tensor product, function space, weakly sequential completeness
Received by editor(s): May 7, 2002
Received by editor(s) in revised form: September 12, 2002
Published electronically: June 11, 2003
Communicated by: N. Tomczak-Jaegermann
Article copyright: © Copyright 2003 American Mathematical Society