Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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

 
 

 

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
DOI: https://doi.org/10.1090/proc/15188
Published electronically: September 11, 2020
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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 [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 46B03, 46B28

Retrieve articles in all journals with MSC (2010): 46B03, 46B28


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
Email: christian.samuel@univ-amu.fr

DOI: https://doi.org/10.1090/proc/15188
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