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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Solution to a problem of Diestel
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by R. M. Causey, E. M. Galego and C. Samuel PDF
Proc. Amer. Math. Soc. 148 (2020), 5261-5267 Request permission


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
  • Email:
  • E. M. Galego
  • Affiliation: Department of Mathematics, IME, University of São Paulo, Rua do Matão 1010, São Paulo, Brazil
  • MR Author ID: 647154
  • Email:
  • C. Samuel
  • Affiliation: Aix Marseille Université, CNRS, Centrale Marseille, I2M, Marseille, France
  • MR Author ID: 153910
  • ORCID: 0000-0001-8607-7719
  • Email:
  • 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
  • © Copyright 2020 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 148 (2020), 5261-5267
  • MSC (2010): Primary 46B03; Secondary 46B28
  • DOI:
  • MathSciNet review: 4163838