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
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 $c_{0} \widehat {\otimes }_\pi c_{0}\widehat {\otimes }_\pi c_{0}$.References
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Additional Information
- R. M. Causey
- Affiliation: Department of Mathematics, Miami University, Oxford, Ohio 45056
- MR Author ID: 923618
- Email: causeyrm@miamioh.edu
- E. M. Galego
- Affiliation: Department of Mathematics, IME, University of São Paulo, Rua do Matão 1010, São Paulo, Brazil
- MR Author ID: 647154
- Email: eloi@ime.usp.br
- C. Samuel
- Affiliation: Aix Marseille Université, CNRS, Centrale Marseille, I2M, Marseille, France
- MR Author ID: 153910
- ORCID: 0000-0001-8607-7719
- Email: christian.samuel@univ-amu.fr
- 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
- 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: https://doi.org/10.1090/proc/15188
- MathSciNet review: 4163838
Dedicated: Dedicated to the memory of Professor Joe Diestel