On the Dunford-Pettis property of the tensor product of $C(K)$ spaces
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- by Fernando Bombal and Ignacio Villanueva PDF
- Proc. Amer. Math. Soc. 129 (2001), 1359-1363 Request permission
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.References
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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
- 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
- © Copyright 2000 American Mathematical Society
- 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
- MathSciNet review: 1712870