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Solution to a problem of Diestel

Authors: R. M. Causey, E. M. Galego and C. Samuel
Journal: Proc. Amer. Math. Soc. 148 (2020), 5261-5267
MSC (2010): Primary 46B03; Secondary 46B28
Published electronically: September 11, 2020
MathSciNet review: 4163838
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Abstract: In the present paper, we prove that the $3$-fold projective tensor product $c_{0} \widehat {\otimes }_\pi c_{0}\widehat {\otimes }_\pi c_{0}$ of $c_0$ is not isomorphic to any subspace of $c_{0} \widehat {\otimes }_\pi c_{0}$. In particular, this settles the long-standing open problem, originally raised by Joe Diestel in a private communication, of whether $c_{0} \widehat {\otimes }_\pi c_{0}$ is isomorphic to $c_{0} \widehat {\otimes }_\pi c_{0}\widehat {\otimes }_\pi c_{0}$.

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Additional Information

R. M. Causey
Affiliation: Department of Mathematics, Miami University, Oxford, Ohio 45056
MR Author ID: 923618

E. M. Galego
Affiliation: Department of Mathematics, IME, University of São Paulo, Rua do Matão 1010, São Paulo, Brazil
MR Author ID: 647154

C. Samuel
Affiliation: Aix Marseille Université, CNRS, Centrale Marseille, I2M, Marseille, France
MR Author ID: 153910
ORCID: 0000-0001-8607-7719

Keywords: 2-asymptotically uniformly smooth space, $c_{0} \widehat {\otimes }_\pi c_{0}$ space, $3$-fold projective tensor product of $c_0$
Received by editor(s): February 17, 2020
Received by editor(s) in revised form: May 17, 2020, and May 18, 2020
Published electronically: September 11, 2020
Dedicated: Dedicated to the memory of Professor Joe Diestel
Communicated by: Stephen Dilworth
Article copyright: © Copyright 2020 American Mathematical Society