Higher projective tensor products of $c_0$
Volume 267 / 2022
Studia Mathematica 267 (2022), 59-107
MSC: Primary 46B03; Secondary 46B28.
DOI: 10.4064/sm210711-3-1
Published online: 26 May 2022
Abstract
Let $m,n$ be positive integers with $m \lt n$. Under certain assumptions on the Banach space $X$, we prove that the $n$-fold projective tensor product of $X$, $\widehat {\otimes }{}^n_\pi X$, is not isomorphic to any subspace of any quotient of the $m$-fold projective tensor product, $\widehat {\otimes }{}_\pi ^m X$. In particular, we prove that $\widehat {\otimes }{}^n_\pi c_0$ is not isomorphic to any subspace of any quotient of $\widehat {\otimes }{}_\pi ^m c_0$. This answers a question from [R. M. Causey et al., Proc. Amer. Math. Soc. 148 (2020)].
