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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

The unit ball of the Hilbert space in its weak topology


Author: Antonio Avilés
Journal: Proc. Amer. Math. Soc. 135 (2007), 833-836
MSC (2000): Primary 46B50, 46B26, 46C05, 54B30, 54D15
Published electronically: September 15, 2006
MathSciNet review: 2262879
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Abstract: We show that the unit ball of $ \ell_p(\Gamma)$ in its weak topology is a continuous image of $ \sigma_1(\Gamma)^\mathbb{N}$, and we deduce some combinatorial properties of its lattice of open sets which are not shared by the balls of other equivalent norms when $ \Gamma$ is uncountable.


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Additional Information

Antonio Avilés
Affiliation: Departamento de Matemáticas, Universidad de Murcia, 30100 Espinardo (Murcia), Spain
Address at time of publication: Equipe de Logique Mathematique, Université de Paris 7, Place Jussieu, 2, 75251 Paris, France
Email: avileslo@um.es

DOI: http://dx.doi.org/10.1090/S0002-9939-06-08527-3
PII: S 0002-9939(06)08527-3
Keywords: Uniform Eberlein compact, polyadic space, $\ell_p$ spaces, Hilbert space, weak topology, equivalent norm
Received by editor(s): March 2, 2005
Received by editor(s) in revised form: October 19, 2005
Published electronically: September 15, 2006
Additional Notes: The author was supported by an FPU grant of MEC of Spain.
Communicated by: N. Tomczak-Jaegermann
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.