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On the Dunford-Pettis property of the tensor product of $C(K)$ spaces


Authors: Fernando Bombal and Ignacio Villanueva
Journal: Proc. Amer. Math. Soc. 129 (2001), 1359-1363
MSC (1991): Primary 46B28, 47B07
DOI: https://doi.org/10.1090/S0002-9939-00-05662-8
Published electronically: October 20, 2000
MathSciNet review: 1712870
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Abstract:

In this paper we characterize those compact Hausdorff spaces $K$such that $C(K)\hat{\otimes}C(K)$ (and $C(K)\hat{\otimes}_s C(K)$) have the Dunford-Pettis Property, answering thus in the negative a question posed by Castillo and González who asked if $\ell_{\infty}\hat{\otimes}\ell_{\infty}$ and $C[0,1]\hat{\otimes}C[0, 1]$ have this property.


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Additional Information

Fernando Bombal
Affiliation: Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad Complutense de Madrid, Madrid 28040, Spain
Email: bombal@eucmax.sim.ucm.es

Ignacio Villanueva
Affiliation: Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad Complutense de Madrid, Madrid 28040, Spain
Email: ignacio_villanueva@mat.ucm.es

DOI: https://doi.org/10.1090/S0002-9939-00-05662-8
Keywords: Dunford-Pettis property, spaces of continuous functions, projective tensor product
Received by editor(s): February 2, 1999
Received by editor(s) in revised form: July 20, 1999
Published electronically: October 20, 2000
Additional Notes: Both authors were partially supported by DGICYT grant PB97-0240.
Communicated by: Dale Alspach
Article copyright: © Copyright 2000 American Mathematical Society