论文标题
$ \ ell_1 $的注射张量
On injective tensor powers of $\ell_1$
论文作者
论文摘要
在本文中，我们证明了$ 3 $ - 折内的张量产品$ \ ell_1 \ wideHat {\ otimes} _ \ varepsilon \ ell_1 \ ell_1 \ wideHat {\ otimes} _ \ \ varepsilon \ varepsilon \ ell_1 $对于任何subsomorphic y subspace os $ \ ell_1 \ wideHat {\ otimes} _ \ varepsilon \ ell_1 $。该结果为$ c_0的投影张量产品提供了一种新的解决方案。此外，此结果意味着，对于任何无限的可计数紧凑型空间$ k，$ 3 $ 3 $ fold-fold的投射张量张量$ c（k）\ wideHat {\ otimes} {\ otimes} {k） $ c（k）\ widehat {\ otimes}_πc（k）$的任何商。
In this paper we prove that the $3$-fold injective tensor product $\ell_1 \widehat{\otimes}_\varepsilon \ell_1 \widehat{\otimes}_\varepsilon \ell_1 $ is not isomorphic to any subspace of $\ell_1 \widehat{\otimes}_\varepsilon \ell_1$. This result provides a new solution to a problem of Diestel on the projective tensor products of $c_0.$ Moreover, this result implies that for any infinite countable compact space $K,$ the $3$-fold projective tensor product $C(K) \widehat{\otimes}_πC(K)\widehat{\otimes}_πC(K)$ is not isomorphic to any quotient of $C(K) \widehat{\otimes}_πC(K)$.
