Higher projective tensor products of
Tom 267 / 2022
Studia Mathematica 267 (2022), 59-107
MSC: Primary 46B03; Secondary 46B28.
DOI: 10.4064/sm210711-3-1
Opublikowany online: 26 May 2022
Streszczenie
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)].
