Abstract
Let $X$ and $Y$ be Banach spaces such that $X$ has an unconditional basis. Then $X \hat{\otimes} Y$, the projective tensor product of $X$ and $Y$, contains no copy of $\ell_1$ if and only if both $X$ and $Y$ contain no copy of $\ell_1$ and each continuous linear operator from $X$ to $Y^\ast$ is compact.
Citation
Xiaoping Xue. Yongjin Li. Qingying Bu. "EMBEDDING $\ell_1$ INTO THE PROJECTIVE TENSOR PRODUCT OF BANACH SPACES." Taiwanese J. Math. 11 (4) 1119 - 1125, 2007. https://doi.org/10.11650/twjm/1500404807
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