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

Emmanuele, G.

doi:10.1090/S0002-9939-1992-1120506-5

Remarks on weak compactness of operators defined on certain injective tensor products
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by G. Emmanuele PDF

Proc. Amer. Math. Soc. 116 (1992), 473-476 Request permission

Addendum: Proc. Amer. Math. Soc. 118 (1993), 335.

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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