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The subprojectivity of the projective tensor product of two $ C(K)$ spaces with $ \Vert K\Vert=\aleph_{0}$


Authors: Elói Medina Galego and Christian Samuel
Journal: Proc. Amer. Math. Soc. 144 (2016), 2611-2617
MSC (2010): Primary 46B03; Secondary 46B25
DOI: https://doi.org/10.1090/proc/12926
Published electronically: October 22, 2015
MathSciNet review: 3477078
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Abstract: We prove that the projective tensor product of two $ C(K)$ spaces, where $ K$ is an infinite countable metric compact space, is $ c_{0}$-saturated and is therefore a subprojective space. This completes some recent work on subprojectivity of projective tensor products involving $ C(K)$ spaces by T. Oikhberg and E. Spinu.


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Elói Medina Galego
Affiliation: Department of Mathematics, University of São Paulo, São Paulo, Brazil 05508-090
Email: eloi@ime.usp.br

Christian Samuel
Affiliation: I2M, Aix Marseille Université, CNRS, UMR 7353, 13453 Marseille Cedex 20, France
Email: christian.samuel@univ-amu.fr

DOI: https://doi.org/10.1090/proc/12926
Keywords: Space of compact operators, spaces of nuclear operators, isomorphic classification, the space $C(\omega^\omega)$
Received by editor(s): April 8, 2015
Received by editor(s) in revised form: August 9, 2015
Published electronically: October 22, 2015
Communicated by: Thomas Schlumprecht
Article copyright: © Copyright 2015 American Mathematical Society