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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Remarks on weak compactness of operators defined on certain injective tensor products


Author: G. Emmanuele
Journal: Proc. Amer. Math. Soc. 116 (1992), 473-476
MSC: Primary 46M05; Secondary 46B28, 47B07
DOI: https://doi.org/10.1090/S0002-9939-1992-1120506-5
Addendum: Proc. Amer. Math. Soc. 118 (1993), null.
MathSciNet review: 1120506
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Abstract: We show that if $ X$ is a $ {\mathcal{L}_\infty }$-space with the Dieudonné property and $ Y$ is a Banach space not containing $ {l_1}$, then any operator $ T:X{ \otimes _\varepsilon }Y \to Z$, where $ Z$ is a weakly sequentially complete Banach space, is weakly compact. Some other results of the same kind are obtained.


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DOI: https://doi.org/10.1090/S0002-9939-1992-1120506-5
Keywords: Weak compactness, injective tensor products
Article copyright: © Copyright 1992 American Mathematical Society