论文标题
$ C_0 $的较高投影张量
Higher projective tensor products of $c_0$
论文作者
论文摘要
令$ m，n $为$ m <n $的正整数。 Under certain assumptions on the Banach space $X$, we prove that the $n$-fold projective tensor product of $X$, $\widehat{\otimes}^n_πX$, is not isomorphic to any subspace of any quotient of the $m$-fold projective tensor product, $\widehat{\otimes}_π^m X$.特别是，我们证明$ \ wideHat {\ otimes}^n_πc_0$与任何商的任何商空间都不是$ \ wideHat {\ otimes}_π^m c_0 $的任何商空间。
Let $m,n$ be positive integers with $m<n$. Under certain assumptions on the Banach space $X$, we prove that the $n$-fold projective tensor product of $X$, $\widehat{\otimes}^n_πX$, is not isomorphic to any subspace of any quotient of the $m$-fold projective tensor product, $\widehat{\otimes}_π^m X$. In particular, we prove that $\widehat{\otimes}^n_πc_0$ is not isomorphic to any subspace of any quotient of $\widehat{\otimes}_π^m c_0$.
