The unit ball of the Hilbert space in its weak topology
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- by Antonio Avilés PDF
- Proc. Amer. Math. Soc. 135 (2007), 833-836 Request permission
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.References
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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
- 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
- © Copyright 2006
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 135 (2007), 833-836
- MSC (2000): Primary 46B50, 46B26, 46C05, 54B30, 54D15
- DOI: https://doi.org/10.1090/S0002-9939-06-08527-3
- MathSciNet review: 2262879