Geodesic
Property $ \bf{(wL)}$ and the reciprocal Dunford-Pettis property in projective tensor products
Commentationes Mathematicae Universitatis Carolinae, Tome 56 (2015) no. 3, pp. 319-329.

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A Banach space $X$ has the reciprocal Dunford-Pettis property ($RDPP$) if every completely continuous operator $T$ from $X$ to any Banach space $Y$ is weakly compact. A Banach space $X$ has the $RDPP$ (resp. property $(wL)$) if every $L$-subset of $X^*$ is relatively weakly compact (resp. weakly precompact). We prove that the projective tensor product $X \otimes{_\pi} Y$ has property $(wL)$ when $X$ has the $RDPP$, $Y$ has property $(wL)$, and $L(X,Y^*)=K(X,Y^*)$.
DOI : 10.14712/1213-7243.2015.126
Classification : 28B05, 46B20, 46B28
Keywords: the reciprocal Dunford-Pettis property; property $(wL)$; spaces of compact operators; weakly precompact sets 
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Ghenciu, Ioana. Property $ \bf{(wL)}$ and the reciprocal Dunford-Pettis property in projective tensor products. Commentationes Mathematicae Universitatis Carolinae, Tome 56 (2015) no. 3, pp. 319-329. doi : 10.14712/1213-7243.2015.126. http://geodesic.mathdoc.fr/articles/10.14712/1213-7243.2015.126/

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